a^2+a=5a+32

Solution for a^2+a=5a+32 equation:

Simplifying
a2 + a = 5a + 32

Reorder the terms:
a + a2 = 5a + 32

Reorder the terms:
a + a2 = 32 + 5a

Solving
a + a2 = 32 + 5a

Solving for variable 'a'.

Reorder the terms:
-32 + a + -5a + a2 = 32 + 5a + -32 + -5a

Combine like terms: a + -5a = -4a
-32 + -4a + a2 = 32 + 5a + -32 + -5a

Reorder the terms:
-32 + -4a + a2 = 32 + -32 + 5a + -5a

Combine like terms: 32 + -32 = 0
-32 + -4a + a2 = 0 + 5a + -5a
-32 + -4a + a2 = 5a + -5a

Combine like terms: 5a + -5a = 0
-32 + -4a + a2 = 0

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}