10n^3-6n=

Solution for 10n^3-6n= equation:

Simplifying
10n3 + -6n = 0

Reorder the terms:
-6n + 10n3 = 0

Solving
-6n + 10n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(-3 + 5n2) = 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 '(-3 + 5n2)' equal to zero and attempt to solve:

Simplifying
-3 + 5n2 = 0

Solving
-3 + 5n2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + 5n2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5n2 = 0 + 3
5n2 = 0 + 3

Combine like terms: 0 + 3 = 3
5n2 = 3

Divide each side by '5'.
n2 = 0.6

Simplifying
n2 = 0.6

Take the square root of each side:
n = {-0.774596669, 0.774596669}
Solution
n = {0, -0.774596669, 0.774596669}