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

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


Simplifying
-4(4b + 2) + -1b(4b + 5) = 0

Reorder the terms:
-4(2 + 4b) + -1b(4b + 5) = 0
(2 * -4 + 4b * -4) + -1b(4b + 5) = 0
(-8 + -16b) + -1b(4b + 5) = 0

Reorder the terms:
-8 + -16b + -1b(5 + 4b) = 0
-8 + -16b + (5 * -1b + 4b * -1b) = 0
-8 + -16b + (-5b + -4b2) = 0

Combine like terms: -16b + -5b = -21b
-8 + -21b + -4b2 = 0

Solving
-8 + -21b + -4b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 21b + 4b2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + 21b + 4b2)' equal to zero and attempt to solve:

Simplifying
8 + 21b + 4b2 = 0

Solving
8 + 21b + 4b2 = 0

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

Divide each side by '4'.
2 + 5.25b + b2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5.25b + -2 + b2 = 0 + -2

Reorder the terms:
2 + -2 + 5.25b + b2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5.25b + b2 = 0 + -2
5.25b + b2 = 0 + -2

Combine like terms: 0 + -2 = -2
5.25b + b2 = -2

The b term is 5.25b.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25b + 6.890625 + b2 = -2 + 6.890625

Reorder the terms:
6.890625 + 5.25b + b2 = -2 + 6.890625

Combine like terms: -2 + 6.890625 = 4.890625
6.890625 + 5.25b + b2 = 4.890625

Factor a perfect square on the left side:
(b + 2.625)(b + 2.625) = 4.890625

Calculate the square root of the right side: 2.211475752

Break this problem into two subproblems by setting 
(b + 2.625) equal to 2.211475752 and -2.211475752.


Subproblem 1
b + 2.625 = 2.211475752

Simplifying
b + 2.625 = 2.211475752

Reorder the terms:
2.625 + b = 2.211475752

Solving
2.625 + b = 2.211475752

Solving for variable 'b'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + b = 2.211475752 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + b = 2.211475752 + -2.625
b = 2.211475752 + -2.625

Combine like terms: 2.211475752 + -2.625 = -0.413524248
b = -0.413524248

Simplifying
b = -0.413524248


Subproblem 2
b + 2.625 = -2.211475752

Simplifying
b + 2.625 = -2.211475752

Reorder the terms:
2.625 + b = -2.211475752

Solving
2.625 + b = -2.211475752

Solving for variable 'b'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + b = -2.211475752 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + b = -2.211475752 + -2.625
b = -2.211475752 + -2.625

Combine like terms: -2.211475752 + -2.625 = -4.836475752
b = -4.836475752

Simplifying
b = -4.836475752


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.413524248, -4.836475752}
Solution
b = {-0.413524248, -4.836475752}

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