-3q^2-24q-45=0

Solution for -3q^2-24q-45=0 equation:

Simplifying
-3q2 + -24q + -45 = 0

Reorder the terms:
-45 + -24q + -3q2 = 0

Solving
-45 + -24q + -3q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(15 + 8q + q2) = 0

Factor a trinomial.
-3((5 + q)(3 + q)) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(5 + q)' equal to zero and attempt to solve:

Simplifying
5 + q = 0

Solving
5 + q = 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 + q = 0 + -5

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

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

Simplifying
q = -5
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 = {-5, -3}