6x(x-3)2=(x-9)(3x)

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Solution for 6x(x-3)2=(x-9)(3x) equation: 


Simplifying
6x(x + -3) * 2 = (x + -9)(3x)

Reorder the terms:
6x(-3 + x) * 2 = (x + -9)(3x)

Reorder the terms for easier multiplication:
6 * 2x(-3 + x) = (x + -9)(3x)

Multiply 6 * 2
12x(-3 + x) = (x + -9)(3x)
(-3 * 12x + x * 12x) = (x + -9)(3x)
(-36x + 12x2) = (x + -9)(3x)

Reorder the terms:
-36x + 12x2 = (-9 + x)(3x)

Remove parenthesis around (3x)
-36x + 12x2 = (-9 + x) * 3x

Reorder the terms for easier multiplication:
-36x + 12x2 = 3x(-9 + x)
-36x + 12x2 = (-9 * 3x + x * 3x)
-36x + 12x2 = (-27x + 3x2)

Solving
-36x + 12x2 = -27x + 3x2

Solving for variable 'x'.

Reorder the terms:
-36x + 27x + 12x2 + -3x2 = -27x + 3x2 + 27x + -3x2

Combine like terms: -36x + 27x = -9x
-9x + 12x2 + -3x2 = -27x + 3x2 + 27x + -3x2

Combine like terms: 12x2 + -3x2 = 9x2
-9x + 9x2 = -27x + 3x2 + 27x + -3x2

Reorder the terms:
-9x + 9x2 = -27x + 27x + 3x2 + -3x2

Combine like terms: -27x + 27x = 0
-9x + 9x2 = 0 + 3x2 + -3x2
-9x + 9x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-9x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9x'.
9x(-1 + x) = 0

Ignore the factor 9.

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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