2n^3+8n^2+12n=0

Solution for 2n^3+8n^2+12n=0 equation:

Simplifying
2n3 + 8n2 + 12n = 0

Reorder the terms:
12n + 8n2 + 2n3 = 0

Solving
12n + 8n2 + 2n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(6 + 4n + n2) = 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 + 4n + n2)' equal to zero and attempt to solve:

Simplifying
6 + 4n + n2 = 0

Solving
6 + 4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 4n + -6 + n2 = 0 + -6

Reorder the terms:
6 + -6 + 4n + n2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 4n + n2 = 0 + -6
4n + n2 = 0 + -6

Combine like terms: 0 + -6 = -6
4n + n2 = -6

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4n + 4 + n2 = -6 + 4

Reorder the terms:
4 + 4n + n2 = -6 + 4

Combine like terms: -6 + 4 = -2
4 + 4n + n2 = -2

Factor a perfect square on the left side:
(n + 2)(n + 2) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}