0=b^2-8b-65

Solution for 0=b^2-8b-65 equation:

Simplifying
0 = b2 + -8b + -65

Reorder the terms:
0 = -65 + -8b + b2

Solving
0 = -65 + -8b + b2

Solving for variable 'b'.

Combine like terms: 0 + 65 = 65
65 + 8b + -1b2 = -65 + -8b + b2 + 65 + 8b + -1b2

Reorder the terms:
65 + 8b + -1b2 = -65 + 65 + -8b + 8b + b2 + -1b2

Combine like terms: -65 + 65 = 0
65 + 8b + -1b2 = 0 + -8b + 8b + b2 + -1b2
65 + 8b + -1b2 = -8b + 8b + b2 + -1b2

Combine like terms: -8b + 8b = 0
65 + 8b + -1b2 = 0 + b2 + -1b2
65 + 8b + -1b2 = b2 + -1b2

Combine like terms: b2 + -1b2 = 0
65 + 8b + -1b2 = 0

Factor a trinomial.
(13 + -1b)(5 + 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 '(5 + b)' equal to zero and attempt to solve:

Simplifying
5 + b = 0

Solving
5 + b = 0

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

Add '-5' to each side of the equation.
5 + -5 + b = 0 + -5

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

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

Simplifying
b = -5
Solution
b = {13, -5}