5a^2=36a+32

Solution for 5a^2=36a+32 equation:

Simplifying
5a2 = 36a + 32

Reorder the terms:
5a2 = 32 + 36a

Solving
5a2 = 32 + 36a

Solving for variable 'a'.

Reorder the terms:
-32 + -36a + 5a2 = 32 + 36a + -32 + -36a

Reorder the terms:
-32 + -36a + 5a2 = 32 + -32 + 36a + -36a

Combine like terms: 32 + -32 = 0
-32 + -36a + 5a2 = 0 + 36a + -36a
-32 + -36a + 5a2 = 36a + -36a

Combine like terms: 36a + -36a = 0
-32 + -36a + 5a2 = 0

Factor a trinomial.
(-4 + -5a)(8 + -1a) = 0

Subproblem 1
Set the factor '(-4 + -5a)' equal to zero and attempt to solve:

Simplifying
-4 + -5a = 0

Solving
-4 + -5a = 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 + -5a = 0 + 4

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

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

Divide each side by '-5'.
a = -0.8

Simplifying
a = -0.8
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 = {-0.8, 8}