6b^2+12b+22=8

Solution for 6b^2+12b+22=8 equation:

Simplifying
6b2 + 12b + 22 = 8

Reorder the terms:
22 + 12b + 6b2 = 8

Solving
22 + 12b + 6b2 = 8

Solving for variable 'b'.

Reorder the terms:
22 + -8 + 12b + 6b2 = 8 + -8

Combine like terms: 22 + -8 = 14
14 + 12b + 6b2 = 8 + -8

Combine like terms: 8 + -8 = 0
14 + 12b + 6b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 6b + 3b2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 6b + 3b2)' equal to zero and attempt to solve:

Simplifying
7 + 6b + 3b2 = 0

Solving
7 + 6b + 3b2 = 0

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

Divide each side by '3'.
2.333333333 + 2b + b2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 2b + -2.333333333 + b2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 2b + b2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 2b + b2 = 0 + -2.333333333
2b + b2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
2b + b2 = -2.333333333

The b term is 2b.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2b + 1 + b2 = -2.333333333 + 1

Reorder the terms:
1 + 2b + b2 = -2.333333333 + 1

Combine like terms: -2.333333333 + 1 = -1.333333333
1 + 2b + b2 = -1.333333333

Factor a perfect square on the left side:
(b + 1)(b + 1) = -1.333333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.