8q^2-8q-96=0

Solution for 8q^2-8q-96=0 equation:

Simplifying
8q2 + -8q + -96 = 0

Reorder the terms:
-96 + -8q + 8q2 = 0

Solving
-96 + -8q + 8q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-12 + -1q + q2) = 0

Factor a trinomial.
8((-3 + -1q)(4 + -1q)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-3 + -1q)' equal to zero and attempt to solve:

Simplifying
-3 + -1q = 0

Solving
-3 + -1q = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1q = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1q = 0 + 3
-1q = 0 + 3

Combine like terms: 0 + 3 = 3
-1q = 3

Divide each side by '-1'.
q = -3

Simplifying
q = -3
Subproblem 2
Set the factor '(4 + -1q)' equal to zero and attempt to solve:

Simplifying
4 + -1q = 0

Solving
4 + -1q = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1q = 0 + -4
-1q = 0 + -4

Combine like terms: 0 + -4 = -4
-1q = -4

Divide each side by '-1'.
q = 4

Simplifying
q = 4
Solution
q = {-3, 4}