6n+3n^2=-6

Solution for 6n+3n^2=-6 equation:

Simplifying
6n + 3n2 = -6

Solving
6n + 3n2 = -6

Solving for variable 'n'.

Reorder the terms:
6 + 6n + 3n2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 6n + 3n2 = 0

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

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

Simplifying
2 + 2n + n2 = 0

Solving
2 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + 2n + n2 = 0 + -2

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

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

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

Add '1' to each side of the equation.
2n + 1 + n2 = -2 + 1

Reorder the terms:
1 + 2n + n2 = -2 + 1

Combine like terms: -2 + 1 = -1
1 + 2n + n2 = -1

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

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.