-a^2=36-12a

Solution for -a^2=36-12a equation:

Simplifying
-1a2 = 36 + -12a

Solving
-1a2 = 36 + -12a

Solving for variable 'a'.

Reorder the terms:
-36 + 12a + -1a2 = 36 + -12a + -36 + 12a

Reorder the terms:
-36 + 12a + -1a2 = 36 + -36 + -12a + 12a

Combine like terms: 36 + -36 = 0
-36 + 12a + -1a2 = 0 + -12a + 12a
-36 + 12a + -1a2 = -12a + 12a

Combine like terms: -12a + 12a = 0
-36 + 12a + -1a2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 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 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

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