0=b^2-9b-52

Solution for 0=b^2-9b-52 equation:

Simplifying
0 = b2 + -9b + -52

Reorder the terms:
0 = -52 + -9b + b2

Solving
0 = -52 + -9b + b2

Solving for variable 'b'.

Combine like terms: 0 + 52 = 52
52 + 9b + -1b2 = -52 + -9b + b2 + 52 + 9b + -1b2

Reorder the terms:
52 + 9b + -1b2 = -52 + 52 + -9b + 9b + b2 + -1b2

Combine like terms: -52 + 52 = 0
52 + 9b + -1b2 = 0 + -9b + 9b + b2 + -1b2
52 + 9b + -1b2 = -9b + 9b + b2 + -1b2

Combine like terms: -9b + 9b = 0
52 + 9b + -1b2 = 0 + b2 + -1b2
52 + 9b + -1b2 = b2 + -1b2

Combine like terms: b2 + -1b2 = 0
52 + 9b + -1b2 = 0

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

Subproblem 1
Set the factor '(13 + -1b)' equal to zero and attempt to solve:

Simplifying
13 + -1b = 0

Solving
13 + -1b = 0

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

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

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

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

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

Simplifying
b = 13
Subproblem 2
Set the factor '(4 + b)' equal to zero and attempt to solve:

Simplifying
4 + b = 0

Solving
4 + b = 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 + b = 0 + -4

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

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

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