-4a^2+56a-96=0

Solution for -4a^2+56a-96=0 equation:

Simplifying
-4a2 + 56a + -96 = 0

Reorder the terms:
-96 + 56a + -4a2 = 0

Solving
-96 + 56a + -4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + 14a + -1a2) = 0

Factor a trinomial.
4((-12 + a)(2 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-12 + a)' equal to zero and attempt to solve:

Simplifying
-12 + a = 0

Solving
-12 + a = 0

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

Add '12' to each side of the equation.
-12 + 12 + a = 0 + 12

Combine like terms: -12 + 12 = 0
0 + a = 0 + 12
a = 0 + 12

Combine like terms: 0 + 12 = 12
a = 12

Simplifying
a = 12
Subproblem 2
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
Solution
a = {12, 2}