12b^2-6b-3=0

Solution for 12b^2-6b-3=0 equation:

Simplifying
12b2 + -6b + -3 = 0

Reorder the terms:
-3 + -6b + 12b2 = 0

Solving
-3 + -6b + 12b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -2b + 4b2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -2b + 4b2)' equal to zero and attempt to solve:

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

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

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

Divide each side by '4'.
-0.25 + -0.5b + b2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.5b + 0.25 + b2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.5b + b2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.5b + b2 = 0 + 0.25
-0.5b + b2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-0.5b + b2 = 0.25

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 = 0.25 + 0.0625

Reorder the terms:
0.0625 + -0.5b + b2 = 0.25 + 0.0625

Combine like terms: 0.25 + 0.0625 = 0.3125
0.0625 + -0.5b + b2 = 0.3125

Factor a perfect square on the left side:
(b + -0.25)(b + -0.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(b + -0.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
b + -0.25 = 0.559016994

Simplifying
b + -0.25 = 0.559016994

Reorder the terms:
-0.25 + b = 0.559016994

Solving
-0.25 + b = 0.559016994

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 = 0.559016994 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + b = 0.559016994 + 0.25
b = 0.559016994 + 0.25

Combine like terms: 0.559016994 + 0.25 = 0.809016994
b = 0.809016994

Simplifying
b = 0.809016994

Subproblem 2
b + -0.25 = -0.559016994

Simplifying
b + -0.25 = -0.559016994

Reorder the terms:
-0.25 + b = -0.559016994

Solving
-0.25 + b = -0.559016994

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 = -0.559016994 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + b = -0.559016994 + 0.25
b = -0.559016994 + 0.25

Combine like terms: -0.559016994 + 0.25 = -0.309016994
b = -0.309016994

Simplifying
b = -0.309016994

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.809016994, -0.309016994}
Solution
b = {0.809016994, -0.309016994}