-3n^4-3n^3-108n^2=0

Solution for -3n^4-3n^3-108n^2=0 equation:

Simplifying
-3n4 + -3n3 + -108n2 = 0

Reorder the terms:
-108n2 + -3n3 + -3n4 = 0

Solving
-108n2 + -3n3 + -3n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-3n2'.
-3n2(36 + n + n2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

Move all terms containing n to the left, all other terms to the right.

Simplifying
n2 = 0

Take the square root of each side:
n = {0}
Subproblem 2
Set the factor '(36 + n + n2)' equal to zero and attempt to solve:

Simplifying
36 + n + n2 = 0

Solving
36 + n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + n + -36 + n2 = 0 + -36

Reorder the terms:
36 + -36 + n + n2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + n + n2 = 0 + -36
n + n2 = 0 + -36

Combine like terms: 0 + -36 = -36
n + n2 = -36

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.
n + 0.25 + n2 = -36 + 0.25

Reorder the terms:
0.25 + n + n2 = -36 + 0.25

Combine like terms: -36 + 0.25 = -35.75
0.25 + n + n2 = -35.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -35.75

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.
Solution
n = {0}