-2b(4b+1)-6b=-100

Solution for -2b(4b+1)-6b=-100 equation:

Simplifying
-2b(4b + 1) + -6b = -100

Reorder the terms:
-2b(1 + 4b) + -6b = -100
(1 * -2b + 4b * -2b) + -6b = -100
(-2b + -8b2) + -6b = -100

Reorder the terms:
-2b + -6b + -8b2 = -100

Combine like terms: -2b + -6b = -8b
-8b + -8b2 = -100

Solving
-8b + -8b2 = -100

Solving for variable 'b'.

Reorder the terms:
100 + -8b + -8b2 = -100 + 100

Combine like terms: -100 + 100 = 0
100 + -8b + -8b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + -2b + -2b2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(25 + -2b + -2b2)' equal to zero and attempt to solve:

Simplifying
25 + -2b + -2b2 = 0

Solving
25 + -2b + -2b2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-12.5 + b + b2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + b + 12.5 + b2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + b + b2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + b + b2 = 0 + 12.5
b + b2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
b + b2 = 12.5

The b term is b.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + b2 = 12.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + b2 = 12.5 + 0.25

Combine like terms: 12.5 + 0.25 = 12.75
1.25 + b2 = 12.75

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 12.75

Calculate the square root of the right side: 3.570714214

Break this problem into two subproblems by setting 
(b + 0.5) equal to 3.570714214 and -3.570714214.

Subproblem 1
b + 0.5 = 3.570714214

Simplifying
b + 0.5 = 3.570714214

Reorder the terms:
0.5 + b = 3.570714214

Solving
0.5 + b = 3.570714214

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = 3.570714214 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 3.570714214 + -0.5
b = 3.570714214 + -0.5

Combine like terms: 3.570714214 + -0.5 = 3.070714214
b = 3.070714214

Simplifying
b = 3.070714214

Subproblem 2
b + 0.5 = -3.570714214

Simplifying
b + 0.5 = -3.570714214

Reorder the terms:
0.5 + b = -3.570714214

Solving
0.5 + b = -3.570714214

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = -3.570714214 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -3.570714214 + -0.5
b = -3.570714214 + -0.5

Combine like terms: -3.570714214 + -0.5 = -4.070714214
b = -4.070714214

Simplifying
b = -4.070714214

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {3.070714214, -4.070714214}
Solution
b = {3.070714214, -4.070714214}