a^2=9a+36

Solution for a^2=9a+36 equation:

Simplifying
a2 = 9a + 36

Reorder the terms:
a2 = 36 + 9a

Solving
a2 = 36 + 9a

Solving for variable 'a'.

Reorder the terms:
-36 + -9a + a2 = 36 + 9a + -36 + -9a

Reorder the terms:
-36 + -9a + a2 = 36 + -36 + 9a + -9a

Combine like terms: 36 + -36 = 0
-36 + -9a + a2 = 0 + 9a + -9a
-36 + -9a + a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
-36 + -9a + a2 = 0

Factor a trinomial.
(-3 + -1a)(12 + -1a) = 0

Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 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 + -1a = 0 + -12

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

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

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {-3, 12}