x^2-4x=3x^2-2x

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Solution for x^2-4x=3x^2-2x equation:


Simplifying
x2 + -4x = 3x2 + -2x

Reorder the terms:
-4x + x2 = 3x2 + -2x

Reorder the terms:
-4x + x2 = -2x + 3x2

Solving
-4x + x2 = -2x + 3x2

Solving for variable 'x'.

Reorder the terms:
-4x + 2x + x2 + -3x2 = -2x + 3x2 + 2x + -3x2

Combine like terms: -4x + 2x = -2x
-2x + x2 + -3x2 = -2x + 3x2 + 2x + -3x2

Combine like terms: x2 + -3x2 = -2x2
-2x + -2x2 = -2x + 3x2 + 2x + -3x2

Reorder the terms:
-2x + -2x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
-2x + -2x2 = 0 + 3x2 + -3x2
-2x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(1 + x) = 0

Ignore the factor -2.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {0, -1}

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