3n^2+6n+18=0

Solution for 3n^2+6n+18=0 equation:

Simplifying
3n2 + 6n + 18 = 0

Reorder the terms:
18 + 6n + 3n2 = 0

Solving
18 + 6n + 3n2 = 0

Solving for variable 'n'.

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

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

Simplifying
6 + 2n + n2 = 0

Solving
6 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 2n + -6 + n2 = 0 + -6

Reorder the terms:
6 + -6 + 2n + n2 = 0 + -6

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

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

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 = -6 + 1

Reorder the terms:
1 + 2n + n2 = -6 + 1

Combine like terms: -6 + 1 = -5
1 + 2n + n2 = -5

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