(q+5)(q+6)=132

Solution for (q+5)(q+6)=132 equation:

Simplifying
(q + 5)(q + 6) = 132

Reorder the terms:
(5 + q)(q + 6) = 132

Reorder the terms:
(5 + q)(6 + q) = 132

Multiply (5 + q) * (6 + q)
(5(6 + q) + q(6 + q)) = 132
((6 * 5 + q * 5) + q(6 + q)) = 132
((30 + 5q) + q(6 + q)) = 132
(30 + 5q + (6 * q + q * q)) = 132
(30 + 5q + (6q + q2)) = 132

Combine like terms: 5q + 6q = 11q
(30 + 11q + q2) = 132

Solving
30 + 11q + q2 = 132

Solving for variable 'q'.

Reorder the terms:
30 + -132 + 11q + q2 = 132 + -132

Combine like terms: 30 + -132 = -102
-102 + 11q + q2 = 132 + -132

Combine like terms: 132 + -132 = 0
-102 + 11q + q2 = 0

Factor a trinomial.
(-17 + -1q)(6 + -1q) = 0

Subproblem 1
Set the factor '(-17 + -1q)' equal to zero and attempt to solve:

Simplifying
-17 + -1q = 0

Solving
-17 + -1q = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1q = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1q = 0 + 17
-1q = 0 + 17

Combine like terms: 0 + 17 = 17
-1q = 17

Divide each side by '-1'.
q = -17

Simplifying
q = -17
Subproblem 2
Set the factor '(6 + -1q)' equal to zero and attempt to solve:

Simplifying
6 + -1q = 0

Solving
6 + -1q = 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 + -1q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1q = 0 + -6
-1q = 0 + -6

Combine like terms: 0 + -6 = -6
-1q = -6

Divide each side by '-1'.
q = 6

Simplifying
q = 6
Solution
q = {-17, 6}