9q^2-9q-54=0

Solution for 9q^2-9q-54=0 equation:

Simplifying
9q2 + -9q + -54 = 0

Reorder the terms:
-54 + -9q + 9q2 = 0

Solving
-54 + -9q + 9q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-6 + -1q + q2) = 0

Factor a trinomial.
9((-2 + -1q)(3 + -1q)) = 0

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

Simplifying
-2 + -1q = 0

Solving
-2 + -1q = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1q = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1q = 0 + 2
-1q = 0 + 2

Combine like terms: 0 + 2 = 2
-1q = 2

Divide each side by '-1'.
q = -2

Simplifying
q = -2
Subproblem 2
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
Solution
q = {-2, 3}