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

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


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

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

Reorder the terms for easier multiplication:
x(-3 + 3x) = (2x)(x + 6)
(-3 * x + 3x * x) = (2x)(x + 6)
(-3x + 3x2) = (2x)(x + 6)

Remove parenthesis around (2x)
-3x + 3x2 = 2x(x + 6)

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

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

Solving for variable 'x'.

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

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

Combine like terms: 3x2 + -2x2 = 1x2
-15x + 1x2 = 12x + 2x2 + -12x + -2x2

Reorder the terms:
-15x + 1x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
-15x + 1x2 = 0 + 2x2 + -2x2
-15x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
-15 + x = 0

Solving
-15 + x = 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 + x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + x = 0 + 15
x = 0 + 15

Combine like terms: 0 + 15 = 15
x = 15

Simplifying
x = 15
Solution
x = {0, 15}

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