=4n^3-2n^2+2n

Solution for =4n^3-2n^2+2n equation:

Simplifying
0 = 4n3 + -2n2 + 2n

Reorder the terms:
0 = 2n + -2n2 + 4n3

Solving
0 = 2n + -2n2 + 4n3

Solving for variable 'n'.
Remove the zero:
-2n + 2n2 + -4n3 = 2n + -2n2 + 4n3 + -2n + 2n2 + -4n3

Reorder the terms:
-2n + 2n2 + -4n3 = 2n + -2n + -2n2 + 2n2 + 4n3 + -4n3

Combine like terms: 2n + -2n = 0
-2n + 2n2 + -4n3 = 0 + -2n2 + 2n2 + 4n3 + -4n3
-2n + 2n2 + -4n3 = -2n2 + 2n2 + 4n3 + -4n3

Combine like terms: -2n2 + 2n2 = 0
-2n + 2n2 + -4n3 = 0 + 4n3 + -4n3
-2n + 2n2 + -4n3 = 4n3 + -4n3

Combine like terms: 4n3 + -4n3 = 0
-2n + 2n2 + -4n3 = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(-1 + n + -2n2) = 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 '(-1 + n + -2n2)' equal to zero and attempt to solve:

Simplifying
-1 + n + -2n2 = 0

Solving
-1 + n + -2n2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
0.5 + -0.5n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -0.5n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -0.5n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -0.5n + n2 = 0 + -0.5
-0.5n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-0.5n + n2 = -0.5

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.5n + 0.25 + n2 = -0.5 + 0.25

Reorder the terms:
0.25 + -0.5n + n2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + -0.5n + n2 = -0.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -0.25

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}