Algebra Calculator with Steps

Choose the algebra mode for your problem

Solve Equation finds values that make one-variable linear or quadratic equations true. A polynomial without an equals sign is interpreted as equal to zero. A number-only expression is evaluated. Simplify & Expand combines terms and distributes brackets; it does not solve for a variable. Factor handles one-variable linear and quadratic expressions. Two-Equation System solves two linear equations in two letters.

The result distinguishes a unique solution, a repeated root, a complex pair, an identity or a contradiction. Systems distinguish a unique intersection, infinitely many pairs and no solution. The displayed substitution checks use the original equation, not just its rearranged form.

Recent inputs are stored in this browser. Clearing browser storage removes that history. A saved link may prefill a worked example, but ordinary typed inputs are not added to the URL.

Worked equation and expression examples

Linear equation: 3x + 2 = 14

Subtract 2 from both sides to obtain 3x = 12. Divide by 3, giving x = 4. Check: 3 × 4 + 2 = 14. The solver shows the exact answer and the values of both original sides.

Quadratic equation: x² − 5x + 6 = 0

The coefficients are a = 1, b = −5 and c = 6. The discriminant is 25 − 24 = 1. Applying the quadratic formula gives (5 ± 1)/2, so x = 3 or x = 2. Each root makes the original left side zero.

Expansion: 2(x + 3) + 4x − 1

Distribute 2, then collect terms: 2x + 6 + 4x − 1 = 6x + 5. This expression still contains x because simplifying is different from solving an equation.

Supported notation and limits

Use parentheses, decimal coefficients, constant fractions, ^ for powers, and implicit multiplication such as 3x or 2(x + 1). Each letter is a separate variable, so xy means x × y. Polynomial simplification supports total degree 8, up to six variables and 128 terms. Solving and full factoring are limited to degree 2 in one variable; systems must be linear in two variables.

Variable denominators and negative variable powers are not accepted in this workspace. Use the Algebraic Fractions Calculator for fractions in x. Use the Expression Calculator to substitute values into several variables, or the Identity Checker to compare polynomial identities.

In Solve Equation mode, number-only expressions may use pi, e and numeric functions such as sqrt(), abs(), sin(), cos(), tan(), log() and ln(). These functions use approximate arithmetic; trig inputs use radians. Constants and functions cannot be mixed with variable equations in this mode. Radicals in quadratic answers are exact forms; displayed decimal roots and the graph are approximations.

Very large or unsupported inputs receive a clear error. The tool does not solve higher-degree equations, nonlinear systems, inequalities or general symbolic functions. Graphs show the rearranged polynomial or two lines and are omitted when a useful bounded plot is unavailable.

Practice and check your working

Try the 20 worked algebra questions to compare your method with a complete solution. The formula reference explains conditions such as a nonzero divisor. The worksheet generator creates fresh questions with printable worked answer keys.

For an equation, substitute into the original sides. For factors, multiply them back out. For fractions, keep the original excluded values. Those checks help identify a sign, grouping or cancellation mistake before the result is used elsewhere.