4b=8(4b)(4b)+4

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

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

Remove parenthesis around (4b)
4b = 8 * 4b(4b) + 4

Remove parenthesis around (4b)
4b = 8 * 4b * 4b + 4

Reorder the terms for easier multiplication:
4b = 8 * 4 * 4b * b + 4

Multiply 8 * 4
4b = 32 * 4b * b + 4

Multiply 32 * 4
4b = 128b * b + 4

Multiply b * b
4b = 128b2 + 4

Reorder the terms:
4b = 4 + 128b2

Solving
4b = 4 + 128b2

Solving for variable 'b'.

Reorder the terms:
-4 + 4b + -128b2 = 4 + 128b2 + -4 + -128b2

Reorder the terms:
-4 + 4b + -128b2 = 4 + -4 + 128b2 + -128b2

Combine like terms: 4 + -4 = 0
-4 + 4b + -128b2 = 0 + 128b2 + -128b2
-4 + 4b + -128b2 = 128b2 + -128b2

Combine like terms: 128b2 + -128b2 = 0
-4 + 4b + -128b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + b + -32b2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + b + -32b2)' equal to zero and attempt to solve:

Simplifying
-1 + b + -32b2 = 0

Solving
-1 + b + -32b2 = 0

Begin completing the square.  Divide all terms by
-32 the coefficient of the squared term: 

Divide each side by '-32'.
0.03125 + -0.03125b + b2 = 0

Move the constant term to the right:

Add '-0.03125' to each side of the equation.
0.03125 + -0.03125b + -0.03125 + b2 = 0 + -0.03125

Reorder the terms:
0.03125 + -0.03125 + -0.03125b + b2 = 0 + -0.03125

Combine like terms: 0.03125 + -0.03125 = 0.00000
0.00000 + -0.03125b + b2 = 0 + -0.03125
-0.03125b + b2 = 0 + -0.03125

Combine like terms: 0 + -0.03125 = -0.03125
-0.03125b + b2 = -0.03125

The b term is b.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.03125b + 0.25 + b2 = -0.03125 + 0.25

Reorder the terms:
0.25 + -0.03125b + b2 = -0.03125 + 0.25

Combine like terms: -0.03125 + 0.25 = 0.21875
0.25 + -0.03125b + b2 = 0.21875

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 0.21875

Calculate the square root of the right side: 0.467707173

Break this problem into two subproblems by setting 
(b + 0.5) equal to 0.467707173 and -0.467707173.

Subproblem 1
b + 0.5 = 0.467707173

Simplifying
b + 0.5 = 0.467707173

Reorder the terms:
0.5 + b = 0.467707173

Solving
0.5 + b = 0.467707173

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = 0.467707173 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 0.467707173 + -0.5
b = 0.467707173 + -0.5

Combine like terms: 0.467707173 + -0.5 = -0.032292827
b = -0.032292827

Simplifying
b = -0.032292827

Subproblem 2
b + 0.5 = -0.467707173

Simplifying
b + 0.5 = -0.467707173

Reorder the terms:
0.5 + b = -0.467707173

Solving
0.5 + b = -0.467707173

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = -0.467707173 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -0.467707173 + -0.5
b = -0.467707173 + -0.5

Combine like terms: -0.467707173 + -0.5 = -0.967707173
b = -0.967707173

Simplifying
b = -0.967707173

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.032292827, -0.967707173}
Solution
b = {-0.032292827, -0.967707173}