15n^3-3n^2+12n=

Solution for 15n^3-3n^2+12n= equation:

Simplifying
15n3 + -3n2 + 12n = 0

Reorder the terms:
12n + -3n2 + 15n3 = 0

Solving
12n + -3n2 + 15n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3n'.
3n(4 + -1n + 5n2) = 0

Ignore the factor 3.
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 '(4 + -1n + 5n2)' equal to zero and attempt to solve:

Simplifying
4 + -1n + 5n2 = 0

Solving
4 + -1n + 5n2 = 0

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

Divide each side by '5'.
0.8 + -0.2n + n2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -0.2n + -0.8 + n2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -0.2n + n2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -0.2n + n2 = 0 + -0.8
-0.2n + n2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-0.2n + n2 = -0.8

The n term is -0.2n.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2n + 0.01 + n2 = -0.8 + 0.01

Reorder the terms:
0.01 + -0.2n + n2 = -0.8 + 0.01

Combine like terms: -0.8 + 0.01 = -0.79
0.01 + -0.2n + n2 = -0.79

Factor a perfect square on the left side:
(n + -0.1)(n + -0.1) = -0.79

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}