(9x-9)(8x+4)=0

Solution for (9x-9)(8x+4)=0 equation:

Simplifying
(9x + -9)(8x + 4) = 0

Reorder the terms:
(-9 + 9x)(8x + 4) = 0

Reorder the terms:
(-9 + 9x)(4 + 8x) = 0

Multiply (-9 + 9x) * (4 + 8x)
(-9(4 + 8x) + 9x * (4 + 8x)) = 0
((4 * -9 + 8x * -9) + 9x * (4 + 8x)) = 0
((-36 + -72x) + 9x * (4 + 8x)) = 0
(-36 + -72x + (4 * 9x + 8x * 9x)) = 0
(-36 + -72x + (36x + 72x2)) = 0

Combine like terms: -72x + 36x = -36x
(-36 + -36x + 72x2) = 0

Solving
-36 + -36x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '36'.
36(-1 + -1x + 2x2) = 0

Factor a trinomial.
36((-1 + -2x)(1 + -1x)) = 0

Ignore the factor 36.
Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
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 = {-0.5, 1}