12a-6a^2=-48

Solution for 12a-6a^2=-48 equation:

Simplifying
12a + -6a2 = -48

Solving
12a + -6a2 = -48

Solving for variable 'a'.

Reorder the terms:
48 + 12a + -6a2 = -48 + 48

Combine like terms: -48 + 48 = 0
48 + 12a + -6a2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + 2a + -1a2) = 0

Factor a trinomial.
6((4 + -1a)(2 + a)) = 0

Ignore the factor 6.
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 '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 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 + a = 0 + -2

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

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

Simplifying
a = -2
Solution
a = {4, -2}