(4x-4)(2x+8)=0

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Solution for (4x-4)(2x+8)=0 equation: 


Simplifying
(4x + -4)(2x + 8) = 0

Reorder the terms:
(-4 + 4x)(2x + 8) = 0

Reorder the terms:
(-4 + 4x)(8 + 2x) = 0

Multiply (-4 + 4x) * (8 + 2x)
(-4(8 + 2x) + 4x * (8 + 2x)) = 0
((8 * -4 + 2x * -4) + 4x * (8 + 2x)) = 0
((-32 + -8x) + 4x * (8 + 2x)) = 0
(-32 + -8x + (8 * 4x + 2x * 4x)) = 0
(-32 + -8x + (32x + 8x2)) = 0

Combine like terms: -8x + 32x = 24x
(-32 + 24x + 8x2) = 0

Solving
-32 + 24x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + 3x + x2) = 0

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

Ignore the factor 8.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-4, 1}

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