6n^4-3n^3+3n^2=

Solution for 6n^4-3n^3+3n^2= equation:

Simplifying
6n4 + -3n3 + 3n2 = 0

Reorder the terms:
3n2 + -3n3 + 6n4 = 0

Solving
3n2 + -3n3 + 6n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3n2'.
3n2(1 + -1n + 2n2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

Move all terms containing n to the left, all other terms to the right.

Simplifying
n2 = 0

Take the square root of each side:
n = {0}
Subproblem 2
Set the factor '(1 + -1n + 2n2)' equal to zero and attempt to solve:

Simplifying
1 + -1n + 2n2 = 0

Solving
1 + -1n + 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 -0.5n.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5n + 0.0625 + n2 = -0.5 + 0.0625

Reorder the terms:
0.0625 + -0.5n + n2 = -0.5 + 0.0625

Combine like terms: -0.5 + 0.0625 = -0.4375
0.0625 + -0.5n + n2 = -0.4375

Factor a perfect square on the left side:
(n + -0.25)(n + -0.25) = -0.4375

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}