12n^2+4n+2=0

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Solution for 12n^2+4n+2=0 equation: 


Simplifying
12n2 + 4n + 2 = 0

Reorder the terms:
2 + 4n + 12n2 = 0

Solving
2 + 4n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 2n + 6n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 2n + 6n2)' equal to zero and attempt to solve:

Simplifying
1 + 2n + 6n2 = 0

Solving
1 + 2n + 6n2 = 0

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

Divide each side by '6'.
0.1666666667 + 0.3333333333n + n2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 0.3333333333n + -0.1666666667 + n2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 0.3333333333n + n2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 0.3333333333n + n2 = 0 + -0.1666666667
0.3333333333n + n2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
0.3333333333n + n2 = -0.1666666667

The n term is 0.3333333333n.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333n + 0.02777777779 + n2 = -0.1666666667 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333n + n2 = -0.1666666667 + 0.02777777779

Combine like terms: -0.1666666667 + 0.02777777779 = -0.13888888891
0.02777777779 + 0.3333333333n + n2 = -0.13888888891

Factor a perfect square on the left side:
(n + 0.1666666667)(n + 0.1666666667) = -0.13888888891

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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