(2x-9)(8x+8)=0

Solution for (2x-9)(8x+8)=0 equation:

Simplifying
(2x + -9)(8x + 8) = 0

Reorder the terms:
(-9 + 2x)(8x + 8) = 0

Reorder the terms:
(-9 + 2x)(8 + 8x) = 0

Multiply (-9 + 2x) * (8 + 8x)
(-9(8 + 8x) + 2x * (8 + 8x)) = 0
((8 * -9 + 8x * -9) + 2x * (8 + 8x)) = 0
((-72 + -72x) + 2x * (8 + 8x)) = 0
(-72 + -72x + (8 * 2x + 8x * 2x)) = 0
(-72 + -72x + (16x + 16x2)) = 0

Combine like terms: -72x + 16x = -56x
(-72 + -56x + 16x2) = 0

Solving
-72 + -56x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-9 + -7x + 2x2) = 0

Factor a trinomial.
8((-1 + -1x)(9 + -2x)) = 0

Ignore the factor 8.
Subproblem 1
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
Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-1, 4.5}