(8x-8)(3x+6)=0

Solution for (8x-8)(3x+6)=0 equation:

Simplifying
(8x + -8)(3x + 6) = 0

Reorder the terms:
(-8 + 8x)(3x + 6) = 0

Reorder the terms:
(-8 + 8x)(6 + 3x) = 0

Multiply (-8 + 8x) * (6 + 3x)
(-8(6 + 3x) + 8x * (6 + 3x)) = 0
((6 * -8 + 3x * -8) + 8x * (6 + 3x)) = 0
((-48 + -24x) + 8x * (6 + 3x)) = 0
(-48 + -24x + (6 * 8x + 3x * 8x)) = 0
(-48 + -24x + (48x + 24x2)) = 0

Combine like terms: -24x + 48x = 24x
(-48 + 24x + 24x2) = 0

Solving
-48 + 24x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24'.
24(-2 + x + x2) = 0

Factor a trinomial.
24((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 24.
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}