4b^2-8b-6=-4

Solution for 4b^2-8b-6=-4 equation:

Simplifying
4b2 + -8b + -6 = -4

Reorder the terms:
-6 + -8b + 4b2 = -4

Solving
-6 + -8b + 4b2 = -4

Solving for variable 'b'.

Reorder the terms:
-6 + 4 + -8b + 4b2 = -4 + 4

Combine like terms: -6 + 4 = -2
-2 + -8b + 4b2 = -4 + 4

Combine like terms: -4 + 4 = 0
-2 + -8b + 4b2 = 0

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

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

Simplifying
-1 + -4b + 2b2 = 0

Solving
-1 + -4b + 2b2 = 0

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

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

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -2b + 0.5 + b2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -2b + b2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -2b + b2 = 0 + 0.5
-2b + b2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-2b + b2 = 0.5

The b term is -2b.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2b + 1 + b2 = 0.5 + 1

Reorder the terms:
1 + -2b + b2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + -2b + b2 = 1.5

Factor a perfect square on the left side:
(b + -1)(b + -1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(b + -1) equal to 1.224744871 and -1.224744871.

Subproblem 1
b + -1 = 1.224744871

Simplifying
b + -1 = 1.224744871

Reorder the terms:
-1 + b = 1.224744871

Solving
-1 + b = 1.224744871

Solving for variable 'b'.

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

Add '1' to each side of the equation.
-1 + 1 + b = 1.224744871 + 1

Combine like terms: -1 + 1 = 0
0 + b = 1.224744871 + 1
b = 1.224744871 + 1

Combine like terms: 1.224744871 + 1 = 2.224744871
b = 2.224744871

Simplifying
b = 2.224744871

Subproblem 2
b + -1 = -1.224744871

Simplifying
b + -1 = -1.224744871

Reorder the terms:
-1 + b = -1.224744871

Solving
-1 + b = -1.224744871

Solving for variable 'b'.

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

Add '1' to each side of the equation.
-1 + 1 + b = -1.224744871 + 1

Combine like terms: -1 + 1 = 0
0 + b = -1.224744871 + 1
b = -1.224744871 + 1

Combine like terms: -1.224744871 + 1 = -0.224744871
b = -0.224744871

Simplifying
b = -0.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {2.224744871, -0.224744871}
Solution
b = {2.224744871, -0.224744871}