4b(b-7)=8b+4

Solution for 4b(b-7)=8b+4 equation:

Simplifying
4b(b + -7) = 8b + 4

Reorder the terms:
4b(-7 + b) = 8b + 4
(-7 * 4b + b * 4b) = 8b + 4
(-28b + 4b2) = 8b + 4

Reorder the terms:
-28b + 4b2 = 4 + 8b

Solving
-28b + 4b2 = 4 + 8b

Solving for variable 'b'.

Reorder the terms:
-4 + -28b + -8b + 4b2 = 4 + 8b + -4 + -8b

Combine like terms: -28b + -8b = -36b
-4 + -36b + 4b2 = 4 + 8b + -4 + -8b

Reorder the terms:
-4 + -36b + 4b2 = 4 + -4 + 8b + -8b

Combine like terms: 4 + -4 = 0
-4 + -36b + 4b2 = 0 + 8b + -8b
-4 + -36b + 4b2 = 8b + -8b

Combine like terms: 8b + -8b = 0
-4 + -36b + 4b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -9b + b2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -9b + b2)' equal to zero and attempt to solve:

Simplifying
-1 + -9b + b2 = 0

Solving
-1 + -9b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -9b + 1 + b2 = 0 + 1

Reorder the terms:
-1 + 1 + -9b + b2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9b + b2 = 0 + 1
-9b + b2 = 0 + 1

Combine like terms: 0 + 1 = 1
-9b + b2 = 1

The b term is -9b.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9b + 20.25 + b2 = 1 + 20.25

Reorder the terms:
20.25 + -9b + b2 = 1 + 20.25

Combine like terms: 1 + 20.25 = 21.25
20.25 + -9b + b2 = 21.25

Factor a perfect square on the left side:
(b + -4.5)(b + -4.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(b + -4.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
b + -4.5 = 4.609772229

Simplifying
b + -4.5 = 4.609772229

Reorder the terms:
-4.5 + b = 4.609772229

Solving
-4.5 + b = 4.609772229

Solving for variable 'b'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + b = 4.609772229 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + b = 4.609772229 + 4.5
b = 4.609772229 + 4.5

Combine like terms: 4.609772229 + 4.5 = 9.109772229
b = 9.109772229

Simplifying
b = 9.109772229

Subproblem 2
b + -4.5 = -4.609772229

Simplifying
b + -4.5 = -4.609772229

Reorder the terms:
-4.5 + b = -4.609772229

Solving
-4.5 + b = -4.609772229

Solving for variable 'b'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + b = -4.609772229 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + b = -4.609772229 + 4.5
b = -4.609772229 + 4.5

Combine like terms: -4.609772229 + 4.5 = -0.109772229
b = -0.109772229

Simplifying
b = -0.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {9.109772229, -0.109772229}
Solution
b = {9.109772229, -0.109772229}