b^2=8b-15

Solution for b^2=8b-15 equation:

Simplifying
b2 = 8b + -15

Reorder the terms:
b2 = -15 + 8b

Solving
b2 = -15 + 8b

Solving for variable 'b'.

Reorder the terms:
15 + -8b + b2 = -15 + 8b + 15 + -8b

Reorder the terms:
15 + -8b + b2 = -15 + 15 + 8b + -8b

Combine like terms: -15 + 15 = 0
15 + -8b + b2 = 0 + 8b + -8b
15 + -8b + b2 = 8b + -8b

Combine like terms: 8b + -8b = 0
15 + -8b + b2 = 0

Factor a trinomial.
(3 + -1b)(5 + -1b) = 0

Subproblem 1
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 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 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {3, 5}