-q^2-12q-27=0

Solution for -q^2-12q-27=0 equation:

Simplifying
-1q2 + -12q + -27 = 0

Reorder the terms:
-27 + -12q + -1q2 = 0

Solving
-27 + -12q + -1q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(27 + 12q + q2) = 0

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

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

Simplifying
9 + q = 0

Solving
9 + q = 0

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

Add '-9' to each side of the equation.
9 + -9 + q = 0 + -9

Combine like terms: 9 + -9 = 0
0 + q = 0 + -9
q = 0 + -9

Combine like terms: 0 + -9 = -9
q = -9

Simplifying
q = -9
Subproblem 2
Set the factor '(3 + q)' equal to zero and attempt to solve:

Simplifying
3 + q = 0

Solving
3 + q = 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 + q = 0 + -3

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

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

Simplifying
q = -3
Solution
q = {-9, -3}