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Equation Solver — Step by Step

Solve linear, quadratic, cubic and higher polynomial equations, rational equations, and equations with roots, exponentials, logs and trig functions. Every answer comes with the working shown.

Use ^ for powers, sqrt(), sin(), ln(), log() (base 10), pi, e. Multiplication can be implied: 3x, 2(x+1).

Try:
Solution
x = 5

Step-by-step solution

  1. Equation
    3(x − 2) = x + 4
  2. Simplify each side
    3x − 6 = x + 4
  3. Move x-terms to the left and numbers to the right
    2x = 10
    Subtract x on both sides; add 6 on both sides.
  4. Divide both sides by 2
    x = 102
  5. Solution
    x = 5
  6. Check
    Substitute x = 5: left side = 9, right side = 9 ✓

What this solver can do

  • Linear equations — collects the variable on one side and shows each move, with exact fractions (no rounding).
  • Quadratics — factors when possible, otherwise uses the quadratic formula and gives exact surds (1 + √2) and complex roots.
  • Cubics and higher — uses the rational root theorem and synthetic division, then solves what is left.
  • Rational equations — clears denominators and rejects extraneous solutions that would divide by zero.
  • Everything else (sin, eˣ, ln, √) — solved numerically to about 10 digits.
System of equations solverFactor, expand & simplifyQuadratic formula calculatorDerivative calculator

Equation solving formulas

Linearax + b = c → x = c − ba
Quadratic formulax = −b ± √b2 − 4ac2a
Zero product propertyIf A·B = 0, then A = 0 or B = 0
Rational root theoremRational roots of anxn + … + a0 have the form pq, p divides a0, q divides an
Exponentialax = b → x = ln bln a

Worked examples

  1. Solve 5x − 7 = 2x + 8.

    1. Subtract 2x: 3x − 7 = 8
    2. Add 7: 3x = 15
    3. Divide by 3

    Answer: x = 5

  2. Solve 2x² − 7x + 3 = 0 by factoring.

    1. (2x − 1)(x − 3) = 0
    2. 2x − 1 = 0 or x − 3 = 0

    Answer: x = ½ or x = 3

  3. Solve 3ˣ = 20.

    1. x = ln 20ln 3 = 2.99571.0986

    Answer: x ≈ 2.7268

  4. Solve √(x + 5) = x − 1.

    1. Square both sides: x + 5 = x2 − 2x + 1
    2. x2 − 3x − 4 = 0 → (x − 4)(x + 1) = 0
    3. Check x = −1: √4 = 2 but −1 − 1 = −2 ✗ (extraneous)

    Answer: x = 4

Tips & common mistakes

  • Whatever you do to one side, do to the other.
  • Squaring both sides or multiplying by an expression containing x can create false (extraneous) solutions — always check.
  • Never divide both sides by x: you lose the solution x = 0. Factor instead.