(8x+16)(8x-8)=0

Solution for (8x+16)(8x-8)=0 equation:

Simplifying
(8x + 16)(8x + -8) = 0

Reorder the terms:
(16 + 8x)(8x + -8) = 0

Reorder the terms:
(16 + 8x)(-8 + 8x) = 0

Multiply (16 + 8x) * (-8 + 8x)
(16(-8 + 8x) + 8x * (-8 + 8x)) = 0
((-8 * 16 + 8x * 16) + 8x * (-8 + 8x)) = 0
((-128 + 128x) + 8x * (-8 + 8x)) = 0
(-128 + 128x + (-8 * 8x + 8x * 8x)) = 0
(-128 + 128x + (-64x + 64x2)) = 0

Combine like terms: 128x + -64x = 64x
(-128 + 64x + 64x2) = 0

Solving
-128 + 64x + 64x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '64'.
64(-2 + x + x2) = 0

Factor a trinomial.
64((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 64.
Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
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 = {-2, 1}