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

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

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

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

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

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

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

Solving
-24 + 24x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24'.
24(-1 + x + 2x2) = 0

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

Ignore the factor 24.
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 '(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
Solution
x = {-1, 0.5}