-3b(-1+4b)=3(-1-3b)

Solution for -3b(-1+4b)=3(-1-3b) equation:

Simplifying
-3b(-1 + 4b) = 3(-1 + -3b)
(-1 * -3b + 4b * -3b) = 3(-1 + -3b)
(3b + -12b2) = 3(-1 + -3b)
3b + -12b2 = (-1 * 3 + -3b * 3)
3b + -12b2 = (-3 + -9b)

Solving
3b + -12b2 = -3 + -9b

Solving for variable 'b'.

Reorder the terms:
3 + 3b + 9b + -12b2 = -3 + -9b + 3 + 9b

Combine like terms: 3b + 9b = 12b
3 + 12b + -12b2 = -3 + -9b + 3 + 9b

Reorder the terms:
3 + 12b + -12b2 = -3 + 3 + -9b + 9b

Combine like terms: -3 + 3 = 0
3 + 12b + -12b2 = 0 + -9b + 9b
3 + 12b + -12b2 = -9b + 9b

Combine like terms: -9b + 9b = 0
3 + 12b + -12b2 = 0

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

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

Simplifying
1 + 4b + -4b2 = 0

Solving
1 + 4b + -4b2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -1b + b2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1b + 0.25 + b2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1b + b2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1b + b2 = 0 + 0.25
-1b + b2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1b + b2 = 0.25

The b term is -1b.  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.
-1b + 0.25 + b2 = 0.25 + 0.25

Reorder the terms:
0.25 + -1b + b2 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
0.25 + -1b + b2 = 0.5

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

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(b + -0.5) equal to 0.707106781 and -0.707106781.

Subproblem 1
b + -0.5 = 0.707106781

Simplifying
b + -0.5 = 0.707106781

Reorder the terms:
-0.5 + b = 0.707106781

Solving
-0.5 + b = 0.707106781

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 = 0.707106781 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + b = 0.707106781 + 0.5
b = 0.707106781 + 0.5

Combine like terms: 0.707106781 + 0.5 = 1.207106781
b = 1.207106781

Simplifying
b = 1.207106781

Subproblem 2
b + -0.5 = -0.707106781

Simplifying
b + -0.5 = -0.707106781

Reorder the terms:
-0.5 + b = -0.707106781

Solving
-0.5 + b = -0.707106781

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 = -0.707106781 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + b = -0.707106781 + 0.5
b = -0.707106781 + 0.5

Combine like terms: -0.707106781 + 0.5 = -0.207106781
b = -0.207106781

Simplifying
b = -0.207106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.207106781, -0.207106781}
Solution
b = {1.207106781, -0.207106781}