(x-2)*(x+2)*x=32x

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Solution for (x-2)*(x+2)*x=32x equation: 


Simplifying
(x + -2)(x + 2) * x = 32x

Reorder the terms:
(-2 + x)(x + 2) * x = 32x

Reorder the terms:
(-2 + x)(2 + x) * x = 32x

Reorder the terms for easier multiplication:
x(-2 + x)(2 + x) = 32x

Multiply (-2 + x) * (2 + x)
x(-2(2 + x) + x(2 + x)) = 32x
x((2 * -2 + x * -2) + x(2 + x)) = 32x
x((-4 + -2x) + x(2 + x)) = 32x
x(-4 + -2x + (2 * x + x * x)) = 32x
x(-4 + -2x + (2x + x2)) = 32x

Combine like terms: -2x + 2x = 0
x(-4 + 0 + x2) = 32x
x(-4 + x2) = 32x
(-4 * x + x2 * x) = 32x
(-4x + x3) = 32x

Solving
-4x + x3 = 32x

Solving for variable 'x'.

Reorder the terms:
-4x + -32x + x3 = 32x + -32x

Combine like terms: -4x + -32x = -36x
-36x + x3 = 32x + -32x

Combine like terms: 32x + -32x = 0
-36x + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-36 + x2) = 0

Factor a difference between two squares.
x((6 + x)(-6 + 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

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

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

Simplifying
x = -6

Subproblem 3
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

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

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Solution
x = {0, -6, 6}

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