9q^2-9q-180=0

Solution for 9q^2-9q-180=0 equation:

Simplifying
9q2 + -9q + -180 = 0

Reorder the terms:
-180 + -9q + 9q2 = 0

Solving
-180 + -9q + 9q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-20 + -1q + q2) = 0

Factor a trinomial.
9((-4 + -1q)(5 + -1q)) = 0

Ignore the factor 9.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1q)' equal to zero and attempt to solve:

Simplifying
5 + -1q = 0

Solving
5 + -1q = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1q = 0 + -5
-1q = 0 + -5

Combine like terms: 0 + -5 = -5
-1q = -5

Divide each side by '-1'.
q = 5

Simplifying
q = 5
Solution
q = {-4, 5}