108q-6q^2-432=0

Solution for 108q-6q^2-432=0 equation:

Simplifying
108q + -6q2 + -432 = 0

Reorder the terms:
-432 + 108q + -6q2 = 0

Solving
-432 + 108q + -6q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-72 + 18q + -1q2) = 0

Factor a trinomial.
6((-12 + q)(6 + -1q)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-12 + q)' equal to zero and attempt to solve:

Simplifying
-12 + q = 0

Solving
-12 + q = 0

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

Add '12' to each side of the equation.
-12 + 12 + q = 0 + 12

Combine like terms: -12 + 12 = 0
0 + q = 0 + 12
q = 0 + 12

Combine like terms: 0 + 12 = 12
q = 12

Simplifying
q = 12
Subproblem 2
Set the factor '(6 + -1q)' equal to zero and attempt to solve:

Simplifying
6 + -1q = 0

Solving
6 + -1q = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1q = 0 + -6
-1q = 0 + -6

Combine like terms: 0 + -6 = -6
-1q = -6

Divide each side by '-1'.
q = 6

Simplifying
q = 6
Solution
q = {12, 6}