3x^4-2x^3+6x^2=0

Solution for 3x^4-2x^3+6x^2=0 equation:

Simplifying
3x4 + -2x3 + 6x2 = 0

Reorder the terms:
6x2 + -2x3 + 3x4 = 0

Solving
6x2 + -2x3 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(6 + -2x + 3x2) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(6 + -2x + 3x2)' equal to zero and attempt to solve:

Simplifying
6 + -2x + 3x2 = 0

Solving
6 + -2x + 3x2 = 0

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

Divide each side by '3'.
2 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -0.6666666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -0.6666666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -0.6666666667x + x2 = 0 + -2
-0.6666666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-0.6666666667x + x2 = -2

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = -2 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -2 + 0.1111111112

Combine like terms: -2 + 0.1111111112 = -1.8888888888
0.1111111112 + -0.6666666667x + x2 = -1.8888888888

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -1.8888888888

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
x = {0}