-3n(n^2+2n)=0

Solution for -3n(n^2+2n)=0 equation:

Simplifying
-3n(n2 + 2n) = 0

Reorder the terms:
-3n(2n + n2) = 0
(2n * -3n + n2 * -3n) = 0
(-6n2 + -3n3) = 0

Solving
-6n2 + -3n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-3n2'.
-3n2(2 + n) = 0

Ignore the factor -3.
Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {0, -2}