(q+8)(q+3)=-6

Solution for (q+8)(q+3)=-6 equation:

Simplifying
(q + 8)(q + 3) = -6

Reorder the terms:
(8 + q)(q + 3) = -6

Reorder the terms:
(8 + q)(3 + q) = -6

Multiply (8 + q) * (3 + q)
(8(3 + q) + q(3 + q)) = -6
((3 * 8 + q * 8) + q(3 + q)) = -6
((24 + 8q) + q(3 + q)) = -6
(24 + 8q + (3 * q + q * q)) = -6
(24 + 8q + (3q + q2)) = -6

Combine like terms: 8q + 3q = 11q
(24 + 11q + q2) = -6

Solving
24 + 11q + q2 = -6

Solving for variable 'q'.

Reorder the terms:
24 + 6 + 11q + q2 = -6 + 6

Combine like terms: 24 + 6 = 30
30 + 11q + q2 = -6 + 6

Combine like terms: -6 + 6 = 0
30 + 11q + q2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
q = {-6, -5}