q^2+22q=-112

Solution for q^2+22q=-112 equation:

Simplifying
q2 + 22q = -112

Reorder the terms:
22q + q2 = -112

Solving
22q + q2 = -112

Solving for variable 'q'.

Reorder the terms:
112 + 22q + q2 = -112 + 112

Combine like terms: -112 + 112 = 0
112 + 22q + q2 = 0

Factor a trinomial.
(14 + q)(8 + q) = 0

Subproblem 1
Set the factor '(14 + q)' equal to zero and attempt to solve:

Simplifying
14 + q = 0

Solving
14 + q = 0

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

Add '-14' to each side of the equation.
14 + -14 + q = 0 + -14

Combine like terms: 14 + -14 = 0
0 + q = 0 + -14
q = 0 + -14

Combine like terms: 0 + -14 = -14
q = -14

Simplifying
q = -14
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 = {-14, -8}