=-4b(-3b-5)-5(-2b-3)

Solution for =-4b(-3b-5)-5(-2b-3) equation:

Simplifying
0 = -4b(-3b + -5) + -5(-2b + -3)

Reorder the terms:
0 = -4b(-5 + -3b) + -5(-2b + -3)
0 = (-5 * -4b + -3b * -4b) + -5(-2b + -3)
0 = (20b + 12b2) + -5(-2b + -3)

Reorder the terms:
0 = 20b + 12b2 + -5(-3 + -2b)
0 = 20b + 12b2 + (-3 * -5 + -2b * -5)
0 = 20b + 12b2 + (15 + 10b)

Reorder the terms:
0 = 15 + 20b + 10b + 12b2

Combine like terms: 20b + 10b = 30b
0 = 15 + 30b + 12b2

Solving
0 = 15 + 30b + 12b2

Solving for variable 'b'.

Combine like terms: 0 + -15 = -15
-15 + -30b + -12b2 = 15 + 30b + 12b2 + -15 + -30b + -12b2

Reorder the terms:
-15 + -30b + -12b2 = 15 + -15 + 30b + -30b + 12b2 + -12b2

Combine like terms: 15 + -15 = 0
-15 + -30b + -12b2 = 0 + 30b + -30b + 12b2 + -12b2
-15 + -30b + -12b2 = 30b + -30b + 12b2 + -12b2

Combine like terms: 30b + -30b = 0
-15 + -30b + -12b2 = 0 + 12b2 + -12b2
-15 + -30b + -12b2 = 12b2 + -12b2

Combine like terms: 12b2 + -12b2 = 0
-15 + -30b + -12b2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(5 + 10b + 4b2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(5 + 10b + 4b2)' equal to zero and attempt to solve:

Simplifying
5 + 10b + 4b2 = 0

Solving
5 + 10b + 4b2 = 0

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

Divide each side by '4'.
1.25 + 2.5b + b2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 2.5b + -1.25 + b2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 2.5b + b2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 2.5b + b2 = 0 + -1.25
2.5b + b2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
2.5b + b2 = -1.25

The b term is 2.5b.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5b + 1.5625 + b2 = -1.25 + 1.5625

Reorder the terms:
1.5625 + 2.5b + b2 = -1.25 + 1.5625

Combine like terms: -1.25 + 1.5625 = 0.3125
1.5625 + 2.5b + b2 = 0.3125

Factor a perfect square on the left side:
(b + 1.25)(b + 1.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(b + 1.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
b + 1.25 = 0.559016994

Simplifying
b + 1.25 = 0.559016994

Reorder the terms:
1.25 + b = 0.559016994

Solving
1.25 + b = 0.559016994

Solving for variable 'b'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + b = 0.559016994 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + b = 0.559016994 + -1.25
b = 0.559016994 + -1.25

Combine like terms: 0.559016994 + -1.25 = -0.690983006
b = -0.690983006

Simplifying
b = -0.690983006

Subproblem 2
b + 1.25 = -0.559016994

Simplifying
b + 1.25 = -0.559016994

Reorder the terms:
1.25 + b = -0.559016994

Solving
1.25 + b = -0.559016994

Solving for variable 'b'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + b = -0.559016994 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + b = -0.559016994 + -1.25
b = -0.559016994 + -1.25

Combine like terms: -0.559016994 + -1.25 = -1.809016994
b = -1.809016994

Simplifying
b = -1.809016994

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.690983006, -1.809016994}
Solution
b = {-0.690983006, -1.809016994}