8b(b+3)=4b-4

Solution for 8b(b+3)=4b-4 equation:

Simplifying
8b(b + 3) = 4b + -4

Reorder the terms:
8b(3 + b) = 4b + -4
(3 * 8b + b * 8b) = 4b + -4
(24b + 8b2) = 4b + -4

Reorder the terms:
24b + 8b2 = -4 + 4b

Solving
24b + 8b2 = -4 + 4b

Solving for variable 'b'.

Reorder the terms:
4 + 24b + -4b + 8b2 = -4 + 4b + 4 + -4b

Combine like terms: 24b + -4b = 20b
4 + 20b + 8b2 = -4 + 4b + 4 + -4b

Reorder the terms:
4 + 20b + 8b2 = -4 + 4 + 4b + -4b

Combine like terms: -4 + 4 = 0
4 + 20b + 8b2 = 0 + 4b + -4b
4 + 20b + 8b2 = 4b + -4b

Combine like terms: 4b + -4b = 0
4 + 20b + 8b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 5b + 2b2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 5b + 2b2)' equal to zero and attempt to solve:

Simplifying
1 + 5b + 2b2 = 0

Solving
1 + 5b + 2b2 = 0

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

Divide each side by '2'.
0.5 + 2.5b + b2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2.5b + -0.5 + b2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2.5b + b2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2.5b + b2 = 0 + -0.5
2.5b + b2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2.5b + b2 = -0.5

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 = -0.5 + 1.5625

Reorder the terms:
1.5625 + 2.5b + b2 = -0.5 + 1.5625

Combine like terms: -0.5 + 1.5625 = 1.0625
1.5625 + 2.5b + b2 = 1.0625

Factor a perfect square on the left side:
(b + 1.25)(b + 1.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(b + 1.25) equal to 1.030776406 and -1.030776406.

Subproblem 1
b + 1.25 = 1.030776406

Simplifying
b + 1.25 = 1.030776406

Reorder the terms:
1.25 + b = 1.030776406

Solving
1.25 + b = 1.030776406

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 = 1.030776406 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + b = 1.030776406 + -1.25
b = 1.030776406 + -1.25

Combine like terms: 1.030776406 + -1.25 = -0.219223594
b = -0.219223594

Simplifying
b = -0.219223594

Subproblem 2
b + 1.25 = -1.030776406

Simplifying
b + 1.25 = -1.030776406

Reorder the terms:
1.25 + b = -1.030776406

Solving
1.25 + b = -1.030776406

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 = -1.030776406 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + b = -1.030776406 + -1.25
b = -1.030776406 + -1.25

Combine like terms: -1.030776406 + -1.25 = -2.280776406
b = -2.280776406

Simplifying
b = -2.280776406

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.219223594, -2.280776406}
Solution
b = {-0.219223594, -2.280776406}