-4a^2+36a-32=0

Solution for -4a^2+36a-32=0 equation:

Simplifying
-4a2 + 36a + -32 = 0

Reorder the terms:
-32 + 36a + -4a2 = 0

Solving
-32 + 36a + -4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 9a + -1a2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-8 + a)' equal to zero and attempt to solve:

Simplifying
-8 + a = 0

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

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

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

Simplifying
a = 8
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Solution
a = {8, 1}