q^2+17q=-72

Solution for q^2+17q=-72 equation:

Simplifying
q2 + 17q = -72

Reorder the terms:
17q + q2 = -72

Solving
17q + q2 = -72

Solving for variable 'q'.

Reorder the terms:
72 + 17q + q2 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + 17q + q2 = 0

Factor a trinomial.
(9 + q)(8 + 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 '(8 + q)' equal to zero and attempt to solve:

Simplifying
8 + q = 0

Solving
8 + q = 0

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

Add '-8' to each side of the equation.
8 + -8 + q = 0 + -8

Combine like terms: 8 + -8 = 0
0 + q = 0 + -8
q = 0 + -8

Combine like terms: 0 + -8 = -8
q = -8

Simplifying
q = -8
Solution
q = {-9, -8}