12n^2+8n^3+6n=

Solution for 12n^2+8n^3+6n= equation:

Simplifying
12n2 + 8n3 + 6n = 0

Reorder the terms:
6n + 12n2 + 8n3 = 0

Solving
6n + 12n2 + 8n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(3 + 6n + 4n2) = 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 + 6n + 4n2)' equal to zero and attempt to solve:

Simplifying
3 + 6n + 4n2 = 0

Solving
3 + 6n + 4n2 = 0

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

Divide each side by '4'.
0.75 + 1.5n + n2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 1.5n + -0.75 + n2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 1.5n + n2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 1.5n + n2 = 0 + -0.75
1.5n + n2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
1.5n + n2 = -0.75

The n term is 1.5n.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5n + 0.5625 + n2 = -0.75 + 0.5625

Reorder the terms:
0.5625 + 1.5n + n2 = -0.75 + 0.5625

Combine like terms: -0.75 + 0.5625 = -0.1875
0.5625 + 1.5n + n2 = -0.1875

Factor a perfect square on the left side:
(n + 0.75)(n + 0.75) = -0.1875

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}