5a^2+12a=32

Solution for 5a^2+12a=32 equation:

Simplifying
5a2 + 12a = 32

Reorder the terms:
12a + 5a2 = 32

Solving
12a + 5a2 = 32

Solving for variable 'a'.

Reorder the terms:
-32 + 12a + 5a2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 12a + 5a2 = 0

Factor a trinomial.
(-4 + -1a)(8 + -5a) = 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 + -5a)' equal to zero and attempt to solve:

Simplifying
8 + -5a = 0

Solving
8 + -5a = 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 + -5a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5a = 0 + -8
-5a = 0 + -8

Combine like terms: 0 + -8 = -8
-5a = -8

Divide each side by '-5'.
a = 1.6

Simplifying
a = 1.6
Solution
a = {-4, 1.6}