b=(11b+14)(8-10b)

Solution for b=(11b+14)(8-10b) equation:

Simplifying
b = (11b + 14)(8 + -10b)

Reorder the terms:
b = (14 + 11b)(8 + -10b)

Multiply (14 + 11b) * (8 + -10b)
b = (14(8 + -10b) + 11b * (8 + -10b))
b = ((8 * 14 + -10b * 14) + 11b * (8 + -10b))
b = ((112 + -140b) + 11b * (8 + -10b))
b = (112 + -140b + (8 * 11b + -10b * 11b))
b = (112 + -140b + (88b + -110b2))

Combine like terms: -140b + 88b = -52b
b = (112 + -52b + -110b2)

Solving
b = 112 + -52b + -110b2

Solving for variable 'b'.

Reorder the terms:
-112 + b + 52b + 110b2 = 112 + -52b + -110b2 + -112 + 52b + 110b2

Combine like terms: b + 52b = 53b
-112 + 53b + 110b2 = 112 + -52b + -110b2 + -112 + 52b + 110b2

Reorder the terms:
-112 + 53b + 110b2 = 112 + -112 + -52b + 52b + -110b2 + 110b2

Combine like terms: 112 + -112 = 0
-112 + 53b + 110b2 = 0 + -52b + 52b + -110b2 + 110b2
-112 + 53b + 110b2 = -52b + 52b + -110b2 + 110b2

Combine like terms: -52b + 52b = 0
-112 + 53b + 110b2 = 0 + -110b2 + 110b2
-112 + 53b + 110b2 = -110b2 + 110b2

Combine like terms: -110b2 + 110b2 = 0
-112 + 53b + 110b2 = 0

Begin completing the square.  Divide all terms by
110 the coefficient of the squared term: 

Divide each side by '110'.
-1.018181818 + 0.4818181818b + b2 = 0

Move the constant term to the right:

Add '1.018181818' to each side of the equation.
-1.018181818 + 0.4818181818b + 1.018181818 + b2 = 0 + 1.018181818

Reorder the terms:
-1.018181818 + 1.018181818 + 0.4818181818b + b2 = 0 + 1.018181818

Combine like terms: -1.018181818 + 1.018181818 = 0.000000000
0.000000000 + 0.4818181818b + b2 = 0 + 1.018181818
0.4818181818b + b2 = 0 + 1.018181818

Combine like terms: 0 + 1.018181818 = 1.018181818
0.4818181818b + b2 = 1.018181818

The b term is 0.4818181818b.  Take half its coefficient (0.2409090909).
Square it (0.05803719008) and add it to both sides.

Add '0.05803719008' to each side of the equation.
0.4818181818b + 0.05803719008 + b2 = 1.018181818 + 0.05803719008

Reorder the terms:
0.05803719008 + 0.4818181818b + b2 = 1.018181818 + 0.05803719008

Combine like terms: 1.018181818 + 0.05803719008 = 1.07621900808
0.05803719008 + 0.4818181818b + b2 = 1.07621900808

Factor a perfect square on the left side:
(b + 0.2409090909)(b + 0.2409090909) = 1.07621900808

Calculate the square root of the right side: 1.037409759

Break this problem into two subproblems by setting 
(b + 0.2409090909) equal to 1.037409759 and -1.037409759.

Subproblem 1
b + 0.2409090909 = 1.037409759

Simplifying
b + 0.2409090909 = 1.037409759

Reorder the terms:
0.2409090909 + b = 1.037409759

Solving
0.2409090909 + b = 1.037409759

Solving for variable 'b'.

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

Add '-0.2409090909' to each side of the equation.
0.2409090909 + -0.2409090909 + b = 1.037409759 + -0.2409090909

Combine like terms: 0.2409090909 + -0.2409090909 = 0.0000000000
0.0000000000 + b = 1.037409759 + -0.2409090909
b = 1.037409759 + -0.2409090909

Combine like terms: 1.037409759 + -0.2409090909 = 0.7965006681
b = 0.7965006681

Simplifying
b = 0.7965006681

Subproblem 2
b + 0.2409090909 = -1.037409759

Simplifying
b + 0.2409090909 = -1.037409759

Reorder the terms:
0.2409090909 + b = -1.037409759

Solving
0.2409090909 + b = -1.037409759

Solving for variable 'b'.

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

Add '-0.2409090909' to each side of the equation.
0.2409090909 + -0.2409090909 + b = -1.037409759 + -0.2409090909

Combine like terms: 0.2409090909 + -0.2409090909 = 0.0000000000
0.0000000000 + b = -1.037409759 + -0.2409090909
b = -1.037409759 + -0.2409090909

Combine like terms: -1.037409759 + -0.2409090909 = -1.2783188499
b = -1.2783188499

Simplifying
b = -1.2783188499

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.7965006681, -1.2783188499}