5n^3-8n^2+6n=

Solution for 5n^3-8n^2+6n= equation:

Simplifying
5n3 + -8n2 + 6n = 0

Reorder the terms:
6n + -8n2 + 5n3 = 0

Solving
6n + -8n2 + 5n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(6 + -8n + 5n2) = 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 '(6 + -8n + 5n2)' equal to zero and attempt to solve:

Simplifying
6 + -8n + 5n2 = 0

Solving
6 + -8n + 5n2 = 0

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

Divide each side by '5'.
1.2 + -1.6n + n2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -1.6n + -1.2 + n2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -1.6n + n2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -1.6n + n2 = 0 + -1.2
-1.6n + n2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-1.6n + n2 = -1.2

The n term is -1.6n.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6n + 0.64 + n2 = -1.2 + 0.64

Reorder the terms:
0.64 + -1.6n + n2 = -1.2 + 0.64

Combine like terms: -1.2 + 0.64 = -0.56
0.64 + -1.6n + n2 = -0.56

Factor a perfect square on the left side:
(n + -0.8)(n + -0.8) = -0.56

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}