(5a^2)-(6a)-32=0

Solution for (5a^2)-(6a)-32=0 equation:

Simplifying
(5a2) + -1(6a) + -32 = 0

Remove parenthesis around (6a)
(5a2) + -1 * 6a + -32 = 0

Multiply -1 * 6
(5a2) + -6a + -32 = 0

Reorder the terms:
-32 + -6a + (5a2) = 0

Solving
-32 + -6a + (5a2) = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -1a)(16 + -5a) = 0

Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve:

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1a = 0 + 2
-1a = 0 + 2

Combine like terms: 0 + 2 = 2
-1a = 2

Divide each side by '-1'.
a = -2

Simplifying
a = -2
Subproblem 2
Set the factor '(16 + -5a)' equal to zero and attempt to solve:

Simplifying
16 + -5a = 0

Solving
16 + -5a = 0

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

Add '-16' to each side of the equation.
16 + -16 + -5a = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -5a = 0 + -16
-5a = 0 + -16

Combine like terms: 0 + -16 = -16
-5a = -16

Divide each side by '-5'.
a = 3.2

Simplifying
a = 3.2
Solution
a = {-2, 3.2}