2n^3=72n

Solution for 2n^3=72n equation:

Simplifying
2n3 = 72n

Solving
2n3 = 72n

Solving for variable 'n'.

Reorder the terms:
-72n + 2n3 = 72n + -72n

Combine like terms: 72n + -72n = 0
-72n + 2n3 = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(-36 + n2) = 0

Factor a difference between two squares.
2n((6 + n)(-6 + 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 '(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}