(a+4)(a+5)=132

Solution for (a+4)(a+5)=132 equation:

Simplifying
(a + 4)(a + 5) = 132

Reorder the terms:
(4 + a)(a + 5) = 132

Reorder the terms:
(4 + a)(5 + a) = 132

Multiply (4 + a) * (5 + a)
(4(5 + a) + a(5 + a)) = 132
((5 * 4 + a * 4) + a(5 + a)) = 132
((20 + 4a) + a(5 + a)) = 132
(20 + 4a + (5 * a + a * a)) = 132
(20 + 4a + (5a + a2)) = 132

Combine like terms: 4a + 5a = 9a
(20 + 9a + a2) = 132

Solving
20 + 9a + a2 = 132

Solving for variable 'a'.

Reorder the terms:
20 + -132 + 9a + a2 = 132 + -132

Combine like terms: 20 + -132 = -112
-112 + 9a + a2 = 132 + -132

Combine like terms: 132 + -132 = 0
-112 + 9a + a2 = 0

Factor a trinomial.
(-16 + -1a)(7 + -1a) = 0

Subproblem 1
Set the factor '(-16 + -1a)' equal to zero and attempt to solve:

Simplifying
-16 + -1a = 0

Solving
-16 + -1a = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1a = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1a = 0 + 16
-1a = 0 + 16

Combine like terms: 0 + 16 = 16
-1a = 16

Divide each side by '-1'.
a = -16

Simplifying
a = -16
Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

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

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

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

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

Simplifying
a = 7
Solution
a = {-16, 7}