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

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


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

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

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

Multiply (-4 + x) * (-4 + 2x)
2(-4(-4 + 2x) + x(-4 + 2x)) = 480
2((-4 * -4 + 2x * -4) + x(-4 + 2x)) = 480
2((16 + -8x) + x(-4 + 2x)) = 480
2(16 + -8x + (-4 * x + 2x * x)) = 480
2(16 + -8x + (-4x + 2x2)) = 480

Combine like terms: -8x + -4x = -12x
2(16 + -12x + 2x2) = 480
(16 * 2 + -12x * 2 + 2x2 * 2) = 480
(32 + -24x + 4x2) = 480

Solving
32 + -24x + 4x2 = 480

Solving for variable 'x'.

Reorder the terms:
32 + -480 + -24x + 4x2 = 480 + -480

Combine like terms: 32 + -480 = -448
-448 + -24x + 4x2 = 480 + -480

Combine like terms: 480 + -480 = 0
-448 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-112 + -6x + x2) = 0

Factor a trinomial.
4((-8 + -1x)(14 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-8, 14}

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