Algebra Calculator — Solve Equations Step by Step
Type in a linear or quadratic equation and get the full solution, not just the answer. Below, you'll also find guidance on inequalities, systems of equations, polynomials, and other algebra problems this tool doesn't solve directly yet.
Enter an equation with x
This solver reads your equation, moves everything to one side, and shows every step it used to isolate x — including the discriminant check for quadratics, so you can see why an equation has two solutions, one, or none.
It currently handles linear equations (like 2x + 3 = 11) and quadratic equations (like x² − 5x + 6 = 0). For systems, inequalities, and polynomial factoring, see the guidance sections below.
Reviewed by Amanda Reeds, Content Researcher · AceCalculator
What an Algebra Calculator Actually Does
An algebra calculator takes an equation containing an unknown variable, such as x, and solves for its value using the rules of algebra: combining like terms, isolating the variable, and applying formulas like the quadratic formula when needed. Students use it to check homework, and anyone can use it to skip repetitive manual solving.
The value isn't just the final number. Seeing each step — standard form, discriminant, the actual arithmetic — is what turns a right answer into an understood one, which matters more the moment a similar problem shows up on a test without a calculator nearby.
Algebra Problems This Page Helps With
Linear Equations
One-step and two-step equations like 2x + 3 = 11 solve instantly in the tool above, with each move — subtract, divide — shown as its own step.
- One-step and two-step equations
- Variables on both sides
Quadratic Equations
The solver above applies the quadratic formula automatically, including complex roots when the discriminant is negative. For a deeper walkthrough of the formula itself, see our dedicated quadratic formula calculator.
- Handles real and complex roots
- Shows the discriminant check
Systems of Equations
Two equations, two unknowns. Solve by substitution (isolate one variable, plug it into the other equation) or elimination (add or subtract equations to cancel a variable).
- Substitution method
- Elimination method
Inequalities
Solve like an equation, but flip the inequality sign when multiplying or dividing by a negative number. Compound inequalities combine two conditions with "and" or "or."
- Single and compound inequalities
- Graphing the solution on a number line
Polynomials
Factor a polynomial to find its roots, multiply two binomials with FOIL, or divide one polynomial by another using long division.
- Factoring and multiplying
- Long division of polynomials
Rational & Exponential Equations
Clear denominators in a rational equation before solving, or take a logarithm of both sides to bring a variable out of an exponent.
- Rational equations and expressions
- Exponential and logarithmic forms
Which Type of Algebra Problem Do You Have?
One equation, one variable, no exponent on x?
That's linear. Type it into the solver above exactly as written, like 5x − 4 = 2x + 11, and it'll isolate x for you with each step shown.
Has an x² term in it?
That's quadratic. The solver applies the quadratic formula and shows the discriminant, so you can see whether the answer is two real roots, one repeated root, or two complex roots.
Two equations that share the same two variables?
That's a system of equations. Solve one equation for a single variable first, then substitute that expression into the other equation to reduce it to one unknown.
Has a <, >, ≤, or ≥ sign instead of an equals sign?
That's an inequality. Solve it the same way as an equation, just remember to flip the inequality sign any time you multiply or divide both sides by a negative number.
Watch Out: Boolean Algebra Isn't the Same Thing
If you're simplifying a logic expression with AND, OR, and NOT on true/false values, that's Boolean algebra, a different branch of math built on logic gates rather than real-number equations. This solver doesn't cover it. Check our other calculators hub for related tools, or search for a dedicated Boolean logic calculator.
Common Algebra Formula Reference
Pro Tip
If the solver above returns "no real solution," that just means the discriminant came out negative. The equation still has two complex answers, which the tool will show using i for the imaginary unit.
About This Calculator
AceCalculator built the solver above to show its work, not just an answer. Every result runs through the same standard-form-then-solve process a teacher would walk through on a whiteboard: combine terms, identify coefficients, apply the right method for the equation's degree.
It's built for linear and quadratic equations specifically, since those cover the bulk of Algebra 1 and Algebra 2 coursework. For everything else on this page — systems, inequalities, polynomials — you'll find explanations and method guidance rather than an automated solve, until dedicated tools are built for those clusters. See our About page for more on how AceCalculator's tools are built and checked.
Who This Page Is For
- Algebra 1 and Algebra 2 students checking homework
- Anyone reviewing math before a placement or entrance test
- Parents helping with algebra homework they haven't touched in years
- Tutors who want a quick step-by-step reference to point to
- Adult learners brushing up on equation-solving basics
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Frequently Asked Questions About Algebra Calculators
Does this algebra calculator show steps?
Yes. For linear equations it shows how the variable gets isolated, and for quadratics it shows the standard form, the discriminant calculation, and how that discriminant leads to the final solution.
How do you solve a quadratic equation?
Rewrite it in standard form ax² + bx + c = 0, then apply the quadratic formula x = (−b ± √(b²−4ac)) / 2a. The value under the square root, called the discriminant, tells you whether the answer is two real solutions, one, or two complex ones.
What does it mean when the discriminant is negative?
A negative discriminant means the equation has no real solutions, only two complex ones involving i, the imaginary unit. Graphically, it means the parabola never crosses the x-axis.
What's the difference between an algebra calculator and a graphing calculator?
An algebra calculator solves for an unknown value symbolically and shows the steps. A graphing calculator plots the equation visually so you can see where it crosses zero or how two functions intersect. Our graphing calculator covers the visual side.
How do you solve a system of equations by substitution?
Solve one equation for a single variable, then substitute that expression into the other equation. This leaves one equation with one unknown, which you solve normally, then plug that value back in to find the second variable.
Is this the same as MathPapa or Mathway?
No, this is AceCalculator's own solver, built independently. MathPapa and Mathway are separate tools with their own step-by-step solvers; all three cover similar linear and quadratic problems, so it's worth comparing outputs if you want a second check.
Does this calculator handle Boolean algebra?
No. Boolean algebra works with true/false logic and operators like AND, OR, and NOT, which is a different system from solving real-number equations. This tool is built for standard algebraic equations, not logic simplification.
Can I solve an inequality the same way as an equation?
Mostly yes. Combine terms and isolate the variable exactly like an equation, but flip the inequality sign any time you multiply or divide both sides by a negative number. That's the one rule that trips people up.
Disclaimer
This tool is for informational and educational purposes only. MathPapa, Mathway, and other named products are trademarks of their respective owners; AceCalculator is not affiliated with or endorsed by them. Always double-check important calculations, especially for graded work.