Simplifying
a^{2} + -12a + 32 = 0
Reorder the terms:
32 + -12a + a^{2} = 0
Solving
32 + -12a + a^{2} = 0
Solving for variable 'a'.
Factor a trinomial.
(4 + -1a)(8 + -1a) = 0
#### Subproblem 1

Set the factor '(4 + -1a)' equal to zero and attempt to solve:
Simplifying
4 + -1a = 0
Solving
4 + -1a = 0
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4
Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4
Combine like terms: 0 + -4 = -4
-1a = -4
Divide each side by '-1'.
a = 4
Simplifying
a = 4
#### Subproblem 2

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#### Solution

a = {4, 8}