480=(x-4)(x-12)(2)

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Solution for 480=(x-4)(x-12)(2) equation: 


Simplifying
480 = (x + -4)(x + -12)(2)

Reorder the terms:
480 = (-4 + x)(x + -12)(2)

Reorder the terms:
480 = (-4 + x)(-12 + x)(2)

Reorder the terms for easier multiplication:
480 = 2(-4 + x)(-12 + x)

Multiply (-4 + x) * (-12 + x)
480 = 2(-4(-12 + x) + x(-12 + x))
480 = 2((-12 * -4 + x * -4) + x(-12 + x))
480 = 2((48 + -4x) + x(-12 + x))
480 = 2(48 + -4x + (-12 * x + x * x))
480 = 2(48 + -4x + (-12x + x2))

Combine like terms: -4x + -12x = -16x
480 = 2(48 + -16x + x2)
480 = (48 * 2 + -16x * 2 + x2 * 2)
480 = (96 + -32x + 2x2)

Solving
480 = 96 + -32x + 2x2

Solving for variable 'x'.

Combine like terms: 480 + -96 = 384
384 + 32x + -2x2 = 96 + -32x + 2x2 + -96 + 32x + -2x2

Reorder the terms:
384 + 32x + -2x2 = 96 + -96 + -32x + 32x + 2x2 + -2x2

Combine like terms: 96 + -96 = 0
384 + 32x + -2x2 = 0 + -32x + 32x + 2x2 + -2x2
384 + 32x + -2x2 = -32x + 32x + 2x2 + -2x2

Combine like terms: -32x + 32x = 0
384 + 32x + -2x2 = 0 + 2x2 + -2x2
384 + 32x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
384 + 32x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(192 + 16x + -1x2) = 0

Factor a trinomial.
2((24 + -1x)(8 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(24 + -1x)' equal to zero and attempt to solve:

Simplifying
24 + -1x = 0

Solving
24 + -1x = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1x = 0 + -24
-1x = 0 + -24

Combine like terms: 0 + -24 = -24
-1x = -24

Divide each side by '-1'.
x = 24

Simplifying
x = 24

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
Solution
x = {24, -8}

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