2n^3=50n

Solution for 2n^3=50n equation:

Simplifying
2n3 = 50n

Solving
2n3 = 50n

Solving for variable 'n'.

Reorder the terms:
-50n + 2n3 = 50n + -50n

Combine like terms: 50n + -50n = 0
-50n + 2n3 = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(-25 + n2) = 0

Factor a difference between two squares.
2n((5 + n)(-5 + n)) = 0

Ignore the factor 2.
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 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 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 + n = 0 + -5

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

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

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

Simplifying
-5 + n = 0

Solving
-5 + n = 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 + n = 0 + 5

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

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

Simplifying
n = 5
Solution
n = {0, -5, 5}