6b^2-12b+68=5

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Solution for 6b^2-12b+68=5 equation: 


Simplifying
6b2 + -12b + 68 = 5

Reorder the terms:
68 + -12b + 6b2 = 5

Solving
68 + -12b + 6b2 = 5

Solving for variable 'b'.

Reorder the terms:
68 + -5 + -12b + 6b2 = 5 + -5

Combine like terms: 68 + -5 = 63
63 + -12b + 6b2 = 5 + -5

Combine like terms: 5 + -5 = 0
63 + -12b + 6b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + -4b + 2b2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(21 + -4b + 2b2)' equal to zero and attempt to solve:

Simplifying
21 + -4b + 2b2 = 0

Solving
21 + -4b + 2b2 = 0

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

Divide each side by '2'.
10.5 + -2b + b2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + -2b + -10.5 + b2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + -2b + b2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + -2b + b2 = 0 + -10.5
-2b + b2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
-2b + b2 = -10.5

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 = -10.5 + 1

Reorder the terms:
1 + -2b + b2 = -10.5 + 1

Combine like terms: -10.5 + 1 = -9.5
1 + -2b + b2 = -9.5

Factor a perfect square on the left side:
(b + -1)(b + -1) = -9.5

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.

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