Simplifying
15b = 11 + -1b2 + 5b

Reorder the terms:
15b = 11 + 5b + -1b2

Solving
15b = 11 + 5b + -1b2

Solving for variable 'b'.

Reorder the terms:
-11 + 15b + -5b + b2 = 11 + 5b + -1b2 + -11 + -5b + b2

Combine like terms: 15b + -5b = 10b
-11 + 10b + b2 = 11 + 5b + -1b2 + -11 + -5b + b2

Reorder the terms:
-11 + 10b + b2 = 11 + -11 + 5b + -5b + -1b2 + b2

Combine like terms: 11 + -11 = 0
-11 + 10b + b2 = 0 + 5b + -5b + -1b2 + b2
-11 + 10b + b2 = 5b + -5b + -1b2 + b2

Combine like terms: 5b + -5b = 0
-11 + 10b + b2 = 0 + -1b2 + b2
-11 + 10b + b2 = -1b2 + b2

Combine like terms: -1b2 + b2 = 0
-11 + 10b + b2 = 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}