-2b(b+5)=-6

Solution for -2b(b+5)=-6 equation:

Simplifying
-2b(b + 5) = -6

Reorder the terms:
-2b(5 + b) = -6
(5 * -2b + b * -2b) = -6
(-10b + -2b2) = -6

Solving
-10b + -2b2 = -6

Solving for variable 'b'.

Reorder the terms:
6 + -10b + -2b2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + -10b + -2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -5b + -1b2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -5b + -1b2)' equal to zero and attempt to solve:

Simplifying
3 + -5b + -1b2 = 0

Solving
3 + -5b + -1b2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + 5b + b2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 5b + 3 + b2 = 0 + 3

Reorder the terms:
-3 + 3 + 5b + b2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5b + b2 = 0 + 3
5b + b2 = 0 + 3

Combine like terms: 0 + 3 = 3
5b + b2 = 3

The b term is 5b.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5b + 6.25 + b2 = 3 + 6.25

Reorder the terms:
6.25 + 5b + b2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + 5b + b2 = 9.25

Factor a perfect square on the left side:
(b + 2.5)(b + 2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(b + 2.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
b + 2.5 = 3.041381265

Simplifying
b + 2.5 = 3.041381265

Reorder the terms:
2.5 + b = 3.041381265

Solving
2.5 + b = 3.041381265

Solving for variable 'b'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + b = 3.041381265 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + b = 3.041381265 + -2.5
b = 3.041381265 + -2.5

Combine like terms: 3.041381265 + -2.5 = 0.541381265
b = 0.541381265

Simplifying
b = 0.541381265

Subproblem 2
b + 2.5 = -3.041381265

Simplifying
b + 2.5 = -3.041381265

Reorder the terms:
2.5 + b = -3.041381265

Solving
2.5 + b = -3.041381265

Solving for variable 'b'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + b = -3.041381265 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + b = -3.041381265 + -2.5
b = -3.041381265 + -2.5

Combine like terms: -3.041381265 + -2.5 = -5.541381265
b = -5.541381265

Simplifying
b = -5.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.541381265, -5.541381265}
Solution
b = {0.541381265, -5.541381265}