=(16-2x)(12-2x)(x)

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Solution for =(16-2x)(12-2x)(x) equation: 


Simplifying
0 = (16 + -2x)(12 + -2x)(x)

Reorder the terms for easier multiplication:
0 = x(16 + -2x)(12 + -2x)

Multiply (16 + -2x) * (12 + -2x)
0 = x(16(12 + -2x) + -2x * (12 + -2x))
0 = x((12 * 16 + -2x * 16) + -2x * (12 + -2x))
0 = x((192 + -32x) + -2x * (12 + -2x))
0 = x(192 + -32x + (12 * -2x + -2x * -2x))
0 = x(192 + -32x + (-24x + 4x2))

Combine like terms: -32x + -24x = -56x
0 = x(192 + -56x + 4x2)
0 = (192 * x + -56x * x + 4x2 * x)
0 = (192x + -56x2 + 4x3)

Solving
0 = 192x + -56x2 + 4x3

Solving for variable 'x'.
Remove the zero:
-192x + 56x2 + -4x3 = 192x + -56x2 + 4x3 + -192x + 56x2 + -4x3

Reorder the terms:
-192x + 56x2 + -4x3 = 192x + -192x + -56x2 + 56x2 + 4x3 + -4x3

Combine like terms: 192x + -192x = 0
-192x + 56x2 + -4x3 = 0 + -56x2 + 56x2 + 4x3 + -4x3
-192x + 56x2 + -4x3 = -56x2 + 56x2 + 4x3 + -4x3

Combine like terms: -56x2 + 56x2 = 0
-192x + 56x2 + -4x3 = 0 + 4x3 + -4x3
-192x + 56x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-192x + 56x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-48 + 14x + -1x2) = 0

Factor a trinomial.
4x((-8 + x)(6 + -1x)) = 0

Ignore the factor 4.

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 '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8

Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, 8, 6}

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