(q+2)(q+3)=132

Solution for (q+2)(q+3)=132 equation:

Simplifying
(q + 2)(q + 3) = 132

Reorder the terms:
(2 + q)(q + 3) = 132

Reorder the terms:
(2 + q)(3 + q) = 132

Multiply (2 + q) * (3 + q)
(2(3 + q) + q(3 + q)) = 132
((3 * 2 + q * 2) + q(3 + q)) = 132
((6 + 2q) + q(3 + q)) = 132
(6 + 2q + (3 * q + q * q)) = 132
(6 + 2q + (3q + q2)) = 132

Combine like terms: 2q + 3q = 5q
(6 + 5q + q2) = 132

Solving
6 + 5q + q2 = 132

Solving for variable 'q'.

Reorder the terms:
6 + -132 + 5q + q2 = 132 + -132

Combine like terms: 6 + -132 = -126
-126 + 5q + q2 = 132 + -132

Combine like terms: 132 + -132 = 0
-126 + 5q + q2 = 0

Factor a trinomial.
(-14 + -1q)(9 + -1q) = 0

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

Simplifying
-14 + -1q = 0

Solving
-14 + -1q = 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 + -1q = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1q = 0 + 14
-1q = 0 + 14

Combine like terms: 0 + 14 = 14
-1q = 14

Divide each side by '-1'.
q = -14

Simplifying
q = -14
Subproblem 2
Set the factor '(9 + -1q)' equal to zero and attempt to solve:

Simplifying
9 + -1q = 0

Solving
9 + -1q = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1q = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1q = 0 + -9
-1q = 0 + -9

Combine like terms: 0 + -9 = -9
-1q = -9

Divide each side by '-1'.
q = 9

Simplifying
q = 9
Solution
q = {-14, 9}