(q+8)(q-6)=-13

Solution for (q+8)(q-6)=-13 equation:

Simplifying
(q + 8)(q + -6) = -13

Reorder the terms:
(8 + q)(q + -6) = -13

Reorder the terms:
(8 + q)(-6 + q) = -13

Multiply (8 + q) * (-6 + q)
(8(-6 + q) + q(-6 + q)) = -13
((-6 * 8 + q * 8) + q(-6 + q)) = -13
((-48 + 8q) + q(-6 + q)) = -13
(-48 + 8q + (-6 * q + q * q)) = -13
(-48 + 8q + (-6q + q2)) = -13

Combine like terms: 8q + -6q = 2q
(-48 + 2q + q2) = -13

Solving
-48 + 2q + q2 = -13

Solving for variable 'q'.

Reorder the terms:
-48 + 13 + 2q + q2 = -13 + 13

Combine like terms: -48 + 13 = -35
-35 + 2q + q2 = -13 + 13

Combine like terms: -13 + 13 = 0
-35 + 2q + q2 = 0

Factor a trinomial.
(-7 + -1q)(5 + -1q) = 0

Subproblem 1
Set the factor '(-7 + -1q)' equal to zero and attempt to solve:

Simplifying
-7 + -1q = 0

Solving
-7 + -1q = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1q = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1q = 0 + 7
-1q = 0 + 7

Combine like terms: 0 + 7 = 7
-1q = 7

Divide each side by '-1'.
q = -7

Simplifying
q = -7
Subproblem 2
Set the factor '(5 + -1q)' equal to zero and attempt to solve:

Simplifying
5 + -1q = 0

Solving
5 + -1q = 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 + -1q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1q = 0 + -5
-1q = 0 + -5

Combine like terms: 0 + -5 = -5
-1q = -5

Divide each side by '-1'.
q = 5

Simplifying
q = 5
Solution
q = {-7, 5}