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

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

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

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

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

Multiply (-8 + 2x) * (8 + 8x)
(-8(8 + 8x) + 2x * (8 + 8x)) = 0
((8 * -8 + 8x * -8) + 2x * (8 + 8x)) = 0
((-64 + -64x) + 2x * (8 + 8x)) = 0
(-64 + -64x + (8 * 2x + 8x * 2x)) = 0
(-64 + -64x + (16x + 16x2)) = 0

Combine like terms: -64x + 16x = -48x
(-64 + -48x + 16x2) = 0

Solving
-64 + -48x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-4 + -3x + x2) = 0

Factor a trinomial.
16((-1 + -1x)(4 + -1x)) = 0

Ignore the factor 16.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-1, 4}