-3n^4-36n^3-108n^2=0

Solution for -3n^4-36n^3-108n^2=0 equation:

Simplifying
-3n4 + -36n3 + -108n2 = 0

Reorder the terms:
-108n2 + -36n3 + -3n4 = 0

Solving
-108n2 + -36n3 + -3n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-3n2'.
-3n2(36 + 12n + n2) = 0

Factor a trinomial.
-3n2((6 + n)(6 + n)) = 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 '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

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

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

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

Simplifying
n = -6
Subproblem 3
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

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

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

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

Simplifying
n = -6
Solution
n = {0, -6, -6}