b^2-b=4b+36

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

Simplifying
b2 + -1b = 4b + 36

Reorder the terms:
-1b + b2 = 4b + 36

Reorder the terms:
-1b + b2 = 36 + 4b

Solving
-1b + b2 = 36 + 4b

Solving for variable 'b'.

Reorder the terms:
-36 + -1b + -4b + b2 = 36 + 4b + -36 + -4b

Combine like terms: -1b + -4b = -5b
-36 + -5b + b2 = 36 + 4b + -36 + -4b

Reorder the terms:
-36 + -5b + b2 = 36 + -36 + 4b + -4b

Combine like terms: 36 + -36 = 0
-36 + -5b + b2 = 0 + 4b + -4b
-36 + -5b + b2 = 4b + -4b

Combine like terms: 4b + -4b = 0
-36 + -5b + b2 = 0

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

Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve:

Simplifying
-4 + -1b = 0

Solving
-4 + -1b = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1b = 0 + 4
-1b = 0 + 4

Combine like terms: 0 + 4 = 4
-1b = 4

Divide each side by '-1'.
b = -4

Simplifying
b = -4
Subproblem 2
Set the factor '(9 + -1b)' equal to zero and attempt to solve:

Simplifying
9 + -1b = 0

Solving
9 + -1b = 0

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

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

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

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

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

Simplifying
b = 9
Solution
b = {-4, 9}