-5+b=-5b(b+1)

Solution for -5+b=-5b(b+1) equation:

Simplifying
-5 + b = -5b(b + 1)

Reorder the terms:
-5 + b = -5b(1 + b)
-5 + b = (1 * -5b + b * -5b)
-5 + b = (-5b + -5b2)

Solving
-5 + b = -5b + -5b2

Solving for variable 'b'.

Combine like terms: b + 5b = 6b
-5 + 6b + 5b2 = -5b + -5b2 + 5b + 5b2

Reorder the terms:
-5 + 6b + 5b2 = -5b + 5b + -5b2 + 5b2

Combine like terms: -5b + 5b = 0
-5 + 6b + 5b2 = 0 + -5b2 + 5b2
-5 + 6b + 5b2 = -5b2 + 5b2

Combine like terms: -5b2 + 5b2 = 0
-5 + 6b + 5b2 = 0

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

Divide each side by '5'.
-1 + 1.2b + b2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.2b + 1 + b2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.2b + b2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.2b + b2 = 0 + 1
1.2b + b2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.2b + b2 = 1

The b term is 1.2b.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2b + 0.36 + b2 = 1 + 0.36

Reorder the terms:
0.36 + 1.2b + b2 = 1 + 0.36

Combine like terms: 1 + 0.36 = 1.36
0.36 + 1.2b + b2 = 1.36

Factor a perfect square on the left side:
(b + 0.6)(b + 0.6) = 1.36

Calculate the square root of the right side: 1.166190379

Break this problem into two subproblems by setting 
(b + 0.6) equal to 1.166190379 and -1.166190379.

Subproblem 1
b + 0.6 = 1.166190379

Simplifying
b + 0.6 = 1.166190379

Reorder the terms:
0.6 + b = 1.166190379

Solving
0.6 + b = 1.166190379

Solving for variable 'b'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + b = 1.166190379 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + b = 1.166190379 + -0.6
b = 1.166190379 + -0.6

Combine like terms: 1.166190379 + -0.6 = 0.566190379
b = 0.566190379

Simplifying
b = 0.566190379

Subproblem 2
b + 0.6 = -1.166190379

Simplifying
b + 0.6 = -1.166190379

Reorder the terms:
0.6 + b = -1.166190379

Solving
0.6 + b = -1.166190379

Solving for variable 'b'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + b = -1.166190379 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + b = -1.166190379 + -0.6
b = -1.166190379 + -0.6

Combine like terms: -1.166190379 + -0.6 = -1.766190379
b = -1.766190379

Simplifying
b = -1.766190379

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.566190379, -1.766190379}