q^2+15q+54=0

Solution for q^2+15q+54=0 equation:

Simplifying
q2 + 15q + 54 = 0

Reorder the terms:
54 + 15q + q2 = 0

Solving
54 + 15q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(9 + q)(6 + q) = 0

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 '(6 + q)' equal to zero and attempt to solve:

Simplifying
6 + q = 0

Solving
6 + q = 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 + q = 0 + -6

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

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

Simplifying
q = -6
Solution
q = {-9, -6}