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

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

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

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

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

Multiply (-6 + 6x) * (9 + 8x)
(-6(9 + 8x) + 6x * (9 + 8x)) = 0
((9 * -6 + 8x * -6) + 6x * (9 + 8x)) = 0
((-54 + -48x) + 6x * (9 + 8x)) = 0
(-54 + -48x + (9 * 6x + 8x * 6x)) = 0
(-54 + -48x + (54x + 48x2)) = 0

Combine like terms: -48x + 54x = 6x
(-54 + 6x + 48x2) = 0

Solving
-54 + 6x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-9 + x + 8x2) = 0

Factor a trinomial.
6((-9 + -8x)(1 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-9 + -8x)' equal to zero and attempt to solve:

Simplifying
-9 + -8x = 0

Solving
-9 + -8x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -8x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -8x = 0 + 9
-8x = 0 + 9

Combine like terms: 0 + 9 = 9
-8x = 9

Divide each side by '-8'.
x = -1.125

Simplifying
x = -1.125
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 = {-1.125, 1}