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

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

Simplifying
3n3 + 8n2 + 12n = 0

Reorder the terms:
12n + 8n2 + 3n3 = 0

Solving
12n + 8n2 + 3n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(12 + 8n + 3n2) = 0

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 '(12 + 8n + 3n2)' equal to zero and attempt to solve:

Simplifying
12 + 8n + 3n2 = 0

Solving
12 + 8n + 3n2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
4 + 2.666666667n + n2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 2.666666667n + -4 + n2 = 0 + -4

Reorder the terms:
4 + -4 + 2.666666667n + n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 2.666666667n + n2 = 0 + -4
2.666666667n + n2 = 0 + -4

Combine like terms: 0 + -4 = -4
2.666666667n + n2 = -4

The n term is 2.666666667n.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667n + 1.777777780 + n2 = -4 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667n + n2 = -4 + 1.777777780

Combine like terms: -4 + 1.777777780 = -2.22222222
1.777777780 + 2.666666667n + n2 = -2.22222222

Factor a perfect square on the left side:
(n + 1.333333334)(n + 1.333333334) = -2.22222222

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}