a^2-13a+32=-8

Solution for a^2-13a+32=-8 equation:

Simplifying
a2 + -13a + 32 = -8

Reorder the terms:
32 + -13a + a2 = -8

Solving
32 + -13a + a2 = -8

Solving for variable 'a'.

Reorder the terms:
32 + 8 + -13a + a2 = -8 + 8

Combine like terms: 32 + 8 = 40
40 + -13a + a2 = -8 + 8

Combine like terms: -8 + 8 = 0
40 + -13a + a2 = 0

Factor a trinomial.
(5 + -1a)(8 + -1a) = 0

Subproblem 1
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
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 = {5, 8}