q^2+6q=-5

Solution for q^2+6q=-5 equation:

Simplifying
q2 + 6q = -5

Reorder the terms:
6q + q2 = -5

Solving
6q + q2 = -5

Solving for variable 'q'.

Reorder the terms:
5 + 6q + q2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 6q + q2 = 0

Factor a trinomial.
(5 + q)(1 + q) = 0

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

Simplifying
1 + q = 0

Solving
1 + q = 0

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

Add '-1' to each side of the equation.
1 + -1 + q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + q = 0 + -1
q = 0 + -1

Combine like terms: 0 + -1 = -1
q = -1

Simplifying
q = -1
Solution
q = {-5, -1}