a^2-a=4a+36

Solution for a^2-a=4a+36 equation:

Simplifying
a2 + -1a = 4a + 36

Reorder the terms:
-1a + a2 = 4a + 36

Reorder the terms:
-1a + a2 = 36 + 4a

Solving
-1a + a2 = 36 + 4a

Solving for variable 'a'.

Reorder the terms:
-36 + -1a + -4a + a2 = 36 + 4a + -36 + -4a

Combine like terms: -1a + -4a = -5a
-36 + -5a + a2 = 36 + 4a + -36 + -4a

Reorder the terms:
-36 + -5a + a2 = 36 + -36 + 4a + -4a

Combine like terms: 36 + -36 = 0
-36 + -5a + a2 = 0 + 4a + -4a
-36 + -5a + a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
-36 + -5a + a2 = 0

Factor a trinomial.
(-4 + -1a)(9 + -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 '(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
Solution
a = {-4, 9}