(x-2)x=3x(2x+1)

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Solution for (x-2)x=3x(2x+1) equation:


Simplifying
(x + -2) * x = 3x(2x + 1)

Reorder the terms:
(-2 + x) * x = 3x(2x + 1)

Reorder the terms for easier multiplication:
x(-2 + x) = 3x(2x + 1)
(-2 * x + x * x) = 3x(2x + 1)
(-2x + x2) = 3x(2x + 1)

Reorder the terms:
-2x + x2 = 3x(1 + 2x)
-2x + x2 = (1 * 3x + 2x * 3x)
-2x + x2 = (3x + 6x2)

Solving
-2x + x2 = 3x + 6x2

Solving for variable 'x'.

Reorder the terms:
-2x + -3x + x2 + -6x2 = 3x + 6x2 + -3x + -6x2

Combine like terms: -2x + -3x = -5x
-5x + x2 + -6x2 = 3x + 6x2 + -3x + -6x2

Combine like terms: x2 + -6x2 = -5x2
-5x + -5x2 = 3x + 6x2 + -3x + -6x2

Reorder the terms:
-5x + -5x2 = 3x + -3x + 6x2 + -6x2

Combine like terms: 3x + -3x = 0
-5x + -5x2 = 0 + 6x2 + -6x2
-5x + -5x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-5x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-5x'.
-5x(1 + x) = 0

Ignore the factor -5.

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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