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

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


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

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

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

Multiply x * x
x2(-3 + 3x) = 2x(x + 6)
(-3 * x2 + 3x * x2) = 2x(x + 6)
(-3x2 + 3x3) = 2x(x + 6)

Reorder the terms:
-3x2 + 3x3 = 2x(6 + x)
-3x2 + 3x3 = (6 * 2x + x * 2x)
-3x2 + 3x3 = (12x + 2x2)

Solving
-3x2 + 3x3 = 12x + 2x2

Solving for variable 'x'.

Reorder the terms:
-12x + -3x2 + -2x2 + 3x3 = 12x + 2x2 + -12x + -2x2

Combine like terms: -3x2 + -2x2 = -5x2
-12x + -5x2 + 3x3 = 12x + 2x2 + -12x + -2x2

Reorder the terms:
-12x + -5x2 + 3x3 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
-12x + -5x2 + 3x3 = 0 + 2x2 + -2x2
-12x + -5x2 + 3x3 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12x + -5x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-12 + -5x + 3x2) = 0

Factor a trinomial.
x((-4 + -3x)(3 + -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 '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -1.333333333, 3}

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