6(3b^2+b-1)=

Solution for 6(3b^2+b-1)= equation:

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

Reorder the terms:
6(-1 + b + 3b2) = 0
(-1 * 6 + b * 6 + 3b2 * 6) = 0
(-6 + 6b + 18b2) = 0

Solving
-6 + 6b + 18b2 = 0

Solving for variable 'b'.

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

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

Simplifying
-1 + b + 3b2 = 0

Solving
-1 + b + 3b2 = 0

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

Divide each side by '3'.
-0.3333333333 + 0.3333333333b + b2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.3333333333b + 0.3333333333 + b2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.3333333333b + b2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.3333333333b + b2 = 0 + 0.3333333333
0.3333333333b + b2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.3333333333b + b2 = 0.3333333333

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.
0.3333333333b + 0.25 + b2 = 0.3333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333b + b2 = 0.3333333333 + 0.25

Combine like terms: 0.3333333333 + 0.25 = 0.5833333333
0.25 + 0.3333333333b + b2 = 0.5833333333

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 0.5833333333

Calculate the square root of the right side: 0.763762616

Break this problem into two subproblems by setting 
(b + 0.5) equal to 0.763762616 and -0.763762616.

Subproblem 1
b + 0.5 = 0.763762616

Simplifying
b + 0.5 = 0.763762616

Reorder the terms:
0.5 + b = 0.763762616

Solving
0.5 + b = 0.763762616

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 = 0.763762616 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 0.763762616 + -0.5
b = 0.763762616 + -0.5

Combine like terms: 0.763762616 + -0.5 = 0.263762616
b = 0.263762616

Simplifying
b = 0.263762616

Subproblem 2
b + 0.5 = -0.763762616

Simplifying
b + 0.5 = -0.763762616

Reorder the terms:
0.5 + b = -0.763762616

Solving
0.5 + b = -0.763762616

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 = -0.763762616 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -0.763762616 + -0.5
b = -0.763762616 + -0.5

Combine like terms: -0.763762616 + -0.5 = -1.263762616
b = -1.263762616

Simplifying
b = -1.263762616

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.263762616, -1.263762616}
Solution
b = {0.263762616, -1.263762616}