4n^5+4n^4-120n^3=0

Solution for 4n^5+4n^4-120n^3=0 equation:

Simplifying
4n5 + 4n4 + -120n3 = 0

Reorder the terms:
-120n3 + 4n4 + 4n5 = 0

Solving
-120n3 + 4n4 + 4n5 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4n3'.
4n3(-30 + n + n2) = 0

Factor a trinomial.
4n3((-6 + -1n)(5 + -1n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'n3' equal to zero and attempt to solve:

Simplifying
n3 = 0

Solving
n3 = 0

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

Simplifying
n3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 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 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 3
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-6, 5}