-8a^2+24a+32=0

Solution for -8a^2+24a+32=0 equation:

Simplifying
-8a2 + 24a + 32 = 0

Reorder the terms:
32 + 24a + -8a2 = 0

Solving
32 + 24a + -8a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '8'.
8(4 + 3a + -1a2) = 0

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

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

Simplifying
1 + a = 0

Solving
1 + a = 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 + a = 0 + -1

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

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

Simplifying
a = -1
Solution
a = {4, -1}