12b^2=-3b-3

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

Simplifying
12b2 = -3b + -3

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

Solving
12b2 = -3 + -3b

Solving for variable 'b'.

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

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

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

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

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

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

Simplifying
1 + b + 4b2 = 0

Solving
1 + b + 4b2 = 0

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

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

Move the constant term to the right:

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

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

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

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

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.
0.25b + 0.25 + b2 = -0.25 + 0.25

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

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

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(b + 0.5) equal to 0.00 and 0.00.

Subproblem 1
b + 0.5 = 0.00

Simplifying
b + 0.5 = 0.00

Reorder the terms:
0.5 + b = 0.00

Solving
0.5 + b = 0.00

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 = 0.00 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 0.00 + -0.5
b = 0.00 + -0.5

Combine like terms: 0.00 + -0.5 = -0.5
b = -0.5

Simplifying
b = -0.5

Subproblem 2
b + 0.5 = 0.00

Simplifying
b + 0.5 = 0.00

Reorder the terms:
0.5 + b = 0.00

Solving
0.5 + b = 0.00

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 = 0.00 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 0.00 + -0.5
b = 0.00 + -0.5

Combine like terms: 0.00 + -0.5 = -0.5
b = -0.5

Simplifying
b = -0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.5, -0.5}
Solution
b = {-0.5, -0.5}