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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}
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