b^2-5b-109=-5

Solution for b^2-5b-109=-5 equation:

Simplifying
b2 + -5b + -109 = -5

Reorder the terms:
-109 + -5b + b2 = -5

Solving
-109 + -5b + b2 = -5

Solving for variable 'b'.

Reorder the terms:
-109 + 5 + -5b + b2 = -5 + 5

Combine like terms: -109 + 5 = -104
-104 + -5b + b2 = -5 + 5

Combine like terms: -5 + 5 = 0
-104 + -5b + b2 = 0

Factor a trinomial.
(-8 + -1b)(13 + -1b) = 0

Subproblem 1
Set the factor '(-8 + -1b)' equal to zero and attempt to solve:

Simplifying
-8 + -1b = 0

Solving
-8 + -1b = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1b = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1b = 0 + 8
-1b = 0 + 8

Combine like terms: 0 + 8 = 8
-1b = 8

Divide each side by '-1'.
b = -8

Simplifying
b = -8
Subproblem 2
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
Solution
b = {-8, 13}