12n^2=-2n-6

Solution for 12n^2=-2n-6 equation:

Simplifying
12n2 = -2n + -6

Reorder the terms:
12n2 = -6 + -2n

Solving
12n2 = -6 + -2n

Solving for variable 'n'.

Reorder the terms:
6 + 2n + 12n2 = -6 + -2n + 6 + 2n

Reorder the terms:
6 + 2n + 12n2 = -6 + 6 + -2n + 2n

Combine like terms: -6 + 6 = 0
6 + 2n + 12n2 = 0 + -2n + 2n
6 + 2n + 12n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
6 + 2n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + n + 6n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + n + 6n2)' equal to zero and attempt to solve:

Simplifying
3 + n + 6n2 = 0

Solving
3 + n + 6n2 = 0

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

Divide each side by '6'.
0.5 + 0.1666666667n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.1666666667n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.1666666667n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.1666666667n + n2 = 0 + -0.5
0.1666666667n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.1666666667n + n2 = -0.5

The n term is n.  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.
0.1666666667n + 0.25 + n2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.1666666667n + n2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.1666666667n + n2 = -0.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -0.25

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.