a^2=9a+52

Solution for a^2=9a+52 equation:

Simplifying
a2 = 9a + 52

Reorder the terms:
a2 = 52 + 9a

Solving
a2 = 52 + 9a

Solving for variable 'a'.

Reorder the terms:
-52 + -9a + a2 = 52 + 9a + -52 + -9a

Reorder the terms:
-52 + -9a + a2 = 52 + -52 + 9a + -9a

Combine like terms: 52 + -52 = 0
-52 + -9a + a2 = 0 + 9a + -9a
-52 + -9a + a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
-52 + -9a + a2 = 0

Factor a trinomial.
(-4 + -1a)(13 + -1a) = 0

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 '(13 + -1a)' equal to zero and attempt to solve:

Simplifying
13 + -1a = 0

Solving
13 + -1a = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1a = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1a = 0 + -13
-1a = 0 + -13

Combine like terms: 0 + -13 = -13
-1a = -13

Divide each side by '-1'.
a = 13

Simplifying
a = 13
Solution
a = {-4, 13}