6n^2-2n=-6

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

Simplifying
6n2 + -2n = -6

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

Solving
-2n + 6n2 = -6

Solving for variable 'n'.

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -1n + 3n2) = 0

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

Simplifying
3 + -1n + 3n2 = 0

Solving
3 + -1n + 3n2 = 0

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

Divide each side by '3'.
1 + -0.3333333333n + n2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -0.3333333333n + -1 + n2 = 0 + -1

Reorder the terms:
1 + -1 + -0.3333333333n + n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.3333333333n + n2 = 0 + -1
-0.3333333333n + n2 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.3333333333n + n2 = -1

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 = -1 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333n + n2 = -1 + 0.02777777779

Combine like terms: -1 + 0.02777777779 = -0.97222222221
0.02777777779 + -0.3333333333n + n2 = -0.97222222221

Factor a perfect square on the left side:
(n + -0.1666666667)(n + -0.1666666667) = -0.97222222221

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.