(5-a)(a+4)+36=

Solution for (5-a)(a+4)+36= equation:

Simplifying
(5 + -1a)(a + 4) + 36 = 0

Reorder the terms:
(5 + -1a)(4 + a) + 36 = 0

Multiply (5 + -1a) * (4 + a)
(5(4 + a) + -1a * (4 + a)) + 36 = 0
((4 * 5 + a * 5) + -1a * (4 + a)) + 36 = 0
((20 + 5a) + -1a * (4 + a)) + 36 = 0
(20 + 5a + (4 * -1a + a * -1a)) + 36 = 0
(20 + 5a + (-4a + -1a2)) + 36 = 0

Combine like terms: 5a + -4a = 1a
(20 + 1a + -1a2) + 36 = 0

Reorder the terms:
20 + 36 + 1a + -1a2 = 0

Combine like terms: 20 + 36 = 56
56 + 1a + -1a2 = 0

Solving
56 + 1a + -1a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(8 + -1a)(7 + a) = 0

Subproblem 1
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Subproblem 2
Set the factor '(7 + a)' equal to zero and attempt to solve:

Simplifying
7 + a = 0

Solving
7 + a = 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 + a = 0 + -7

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

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

Simplifying
a = -7
Solution
a = {8, -7}