n^3=5n

Solution for n^3=5n equation:

Simplifying
n3 = 5n

Solving
n3 = 5n

Solving for variable 'n'.

Reorder the terms:
-5n + n3 = 5n + -5n

Combine like terms: 5n + -5n = 0
-5n + n3 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5 + n2) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-5 + n2)' equal to zero and attempt to solve:

Simplifying
-5 + n2 = 0

Solving
-5 + n2 = 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 + n2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + n2 = 0 + 5
n2 = 0 + 5

Combine like terms: 0 + 5 = 5
n2 = 5

Simplifying
n2 = 5

Take the square root of each side:
n = {-2.236067978, 2.236067978}
Solution
n = {0, -2.236067978, 2.236067978}