-4a=a^2-12

Solution for -4a=a^2-12 equation:

Simplifying
-4a = a2 + -12

Reorder the terms:
-4a = -12 + a2

Solving
-4a = -12 + a2

Solving for variable 'a'.

Reorder the terms:
12 + -4a + -1a2 = -12 + a2 + 12 + -1a2

Reorder the terms:
12 + -4a + -1a2 = -12 + 12 + a2 + -1a2

Combine like terms: -12 + 12 = 0
12 + -4a + -1a2 = 0 + a2 + -1a2
12 + -4a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
12 + -4a + -1a2 = 0

Factor a trinomial.
(2 + -1a)(6 + a) = 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 '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

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

Add '-6' to each side of the equation.
6 + -6 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Solution
a = {2, -6}