(4x-4)(4x-4)=256

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Solution for (4x-4)(4x-4)=256 equation: 


Simplifying
(4x + -4)(4x + -4) = 256

Reorder the terms:
(-4 + 4x)(4x + -4) = 256

Reorder the terms:
(-4 + 4x)(-4 + 4x) = 256

Multiply (-4 + 4x) * (-4 + 4x)
(-4(-4 + 4x) + 4x * (-4 + 4x)) = 256
((-4 * -4 + 4x * -4) + 4x * (-4 + 4x)) = 256
((16 + -16x) + 4x * (-4 + 4x)) = 256
(16 + -16x + (-4 * 4x + 4x * 4x)) = 256
(16 + -16x + (-16x + 16x2)) = 256

Combine like terms: -16x + -16x = -32x
(16 + -32x + 16x2) = 256

Solving
16 + -32x + 16x2 = 256

Solving for variable 'x'.

Reorder the terms:
16 + -256 + -32x + 16x2 = 256 + -256

Combine like terms: 16 + -256 = -240
-240 + -32x + 16x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-240 + -32x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-15 + -2x + x2) = 0

Factor a trinomial.
16((-3 + -1x)(5 + -1x)) = 0

Ignore the factor 16.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}

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