a^2=36-5a

Solution for a^2=36-5a equation:

Simplifying
a2 = 36 + -5a

Solving
a2 = 36 + -5a

Solving for variable 'a'.

Reorder the terms:
-36 + 5a + a2 = 36 + -5a + -36 + 5a

Reorder the terms:
-36 + 5a + a2 = 36 + -36 + -5a + 5a

Combine like terms: 36 + -36 = 0
-36 + 5a + a2 = 0 + -5a + 5a
-36 + 5a + a2 = -5a + 5a

Combine like terms: -5a + 5a = 0
-36 + 5a + a2 = 0

Factor a trinomial.
(-9 + -1a)(4 + -1a) = 0

Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
Subproblem 2
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
Solution
a = {-9, 4}