Simplifying
15b = 11 + -1b^{2} + 5b
Reorder the terms:
15b = 11 + 5b + -1b^{2}
Solving
15b = 11 + 5b + -1b^{2}
Solving for variable 'b'.
Reorder the terms:
-11 + 15b + -5b + b^{2} = 11 + 5b + -1b^{2} + -11 + -5b + b^{2}
Combine like terms: 15b + -5b = 10b
-11 + 10b + b^{2} = 11 + 5b + -1b^{2} + -11 + -5b + b^{2}
Reorder the terms:
-11 + 10b + b^{2} = 11 + -11 + 5b + -5b + -1b^{2} + b^{2}
Combine like terms: 11 + -11 = 0
-11 + 10b + b^{2} = 0 + 5b + -5b + -1b^{2} + b^{2}
-11 + 10b + b^{2} = 5b + -5b + -1b^{2} + b^{2}
Combine like terms: 5b + -5b = 0
-11 + 10b + b^{2} = 0 + -1b^{2} + b^{2}
-11 + 10b + b^{2} = -1b^{2} + b^{2}
Combine like terms: -1b^{2} + b^{2} = 0
-11 + 10b + b^{2} = 0
Factor a trinomial.
(-11 + -1b)(1 + -1b) = 0
#### Subproblem 1

Set the factor '(-11 + -1b)' equal to zero and attempt to solve:
Simplifying
-11 + -1b = 0
Solving
-11 + -1b = 0
Move all terms containing b to the left, all other terms to the right.
Add '11' to each side of the equation.
-11 + 11 + -1b = 0 + 11
Combine like terms: -11 + 11 = 0
0 + -1b = 0 + 11
-1b = 0 + 11
Combine like terms: 0 + 11 = 11
-1b = 11
Divide each side by '-1'.
b = -11
Simplifying
b = -11
#### Subproblem 2

Set the factor '(1 + -1b)' equal to zero and attempt to solve:
Simplifying
1 + -1b = 0
Solving
1 + -1b = 0
Move all terms containing b to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1b = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1b = 0 + -1
-1b = 0 + -1
Combine like terms: 0 + -1 = -1
-1b = -1
Divide each side by '-1'.
b = 1
Simplifying
b = 1#### Solution

b = {-11, 1}