(8x-8)(6x+9)=0

Solution for (8x-8)(6x+9)=0 equation:

Simplifying
(8x + -8)(6x + 9) = 0

Reorder the terms:
(-8 + 8x)(6x + 9) = 0

Reorder the terms:
(-8 + 8x)(9 + 6x) = 0

Multiply (-8 + 8x) * (9 + 6x)
(-8(9 + 6x) + 8x * (9 + 6x)) = 0
((9 * -8 + 6x * -8) + 8x * (9 + 6x)) = 0
((-72 + -48x) + 8x * (9 + 6x)) = 0
(-72 + -48x + (9 * 8x + 6x * 8x)) = 0
(-72 + -48x + (72x + 48x2)) = 0

Combine like terms: -48x + 72x = 24x
(-72 + 24x + 48x2) = 0

Solving
-72 + 24x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24'.
24(-3 + x + 2x2) = 0

Factor a trinomial.
24((-3 + -2x)(1 + -1x)) = 0

Ignore the factor 24.
Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, 1}