(2x)(x+6)=(3x-3)(x)

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Solution for (2x)(x+6)=(3x-3)(x) equation:


Simplifying
(2x)(x + 6) = (3x + -3)(x)

Remove parenthesis around (2x)
2x(x + 6) = (3x + -3)(x)

Reorder the terms:
2x(6 + x) = (3x + -3)(x)
(6 * 2x + x * 2x) = (3x + -3)(x)
(12x + 2x2) = (3x + -3)(x)

Reorder the terms:
12x + 2x2 = (-3 + 3x)(x)

Reorder the terms for easier multiplication:
12x + 2x2 = x(-3 + 3x)
12x + 2x2 = (-3 * x + 3x * x)
12x + 2x2 = (-3x + 3x2)

Solving
12x + 2x2 = -3x + 3x2

Solving for variable 'x'.

Reorder the terms:
12x + 3x + 2x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: 12x + 3x = 15x
15x + 2x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
15x + -1x2 = -3x + 3x2 + 3x + -3x2

Reorder the terms:
15x + -1x2 = -3x + 3x + 3x2 + -3x2

Combine like terms: -3x + 3x = 0
15x + -1x2 = 0 + 3x2 + -3x2
15x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
15x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + -1x) = 0

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 '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15

Solution

x = {0, 15}

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