4=2(2b+1)6b

Solution for 4=2(2b+1)6b equation:

Simplifying
4 = 2(2b + 1) * 6b

Reorder the terms:
4 = 2(1 + 2b) * 6b

Reorder the terms for easier multiplication:
4 = 2 * 6b(1 + 2b)

Multiply 2 * 6
4 = 12b(1 + 2b)
4 = (1 * 12b + 2b * 12b)
4 = (12b + 24b2)

Solving
4 = 12b + 24b2

Solving for variable 'b'.

Reorder the terms:
4 + -12b + -24b2 = 12b + -12b + 24b2 + -24b2

Combine like terms: 12b + -12b = 0
4 + -12b + -24b2 = 0 + 24b2 + -24b2
4 + -12b + -24b2 = 24b2 + -24b2

Combine like terms: 24b2 + -24b2 = 0
4 + -12b + -24b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -3b + -6b2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -3b + -6b2)' equal to zero and attempt to solve:

Simplifying
1 + -3b + -6b2 = 0

Solving
1 + -3b + -6b2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.1666666667 + 0.5b + b2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.5b + 0.1666666667 + b2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 0.5b + b2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 0.5b + b2 = 0 + 0.1666666667
0.5b + b2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
0.5b + b2 = 0.1666666667

The b term is 0.5b.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5b + 0.0625 + b2 = 0.1666666667 + 0.0625

Reorder the terms:
0.0625 + 0.5b + b2 = 0.1666666667 + 0.0625

Combine like terms: 0.1666666667 + 0.0625 = 0.2291666667
0.0625 + 0.5b + b2 = 0.2291666667

Factor a perfect square on the left side:
(b + 0.25)(b + 0.25) = 0.2291666667

Calculate the square root of the right side: 0.478713554

Break this problem into two subproblems by setting 
(b + 0.25) equal to 0.478713554 and -0.478713554.

Subproblem 1
b + 0.25 = 0.478713554

Simplifying
b + 0.25 = 0.478713554

Reorder the terms:
0.25 + b = 0.478713554

Solving
0.25 + b = 0.478713554

Solving for variable 'b'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + b = 0.478713554 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + b = 0.478713554 + -0.25
b = 0.478713554 + -0.25

Combine like terms: 0.478713554 + -0.25 = 0.228713554
b = 0.228713554

Simplifying
b = 0.228713554

Subproblem 2
b + 0.25 = -0.478713554

Simplifying
b + 0.25 = -0.478713554

Reorder the terms:
0.25 + b = -0.478713554

Solving
0.25 + b = -0.478713554

Solving for variable 'b'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + b = -0.478713554 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + b = -0.478713554 + -0.25
b = -0.478713554 + -0.25

Combine like terms: -0.478713554 + -0.25 = -0.728713554
b = -0.728713554

Simplifying
b = -0.728713554

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.228713554, -0.728713554}
Solution
b = {0.228713554, -0.728713554}