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

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

Simplifying
6x3 + -1x2 + x = 0

Reorder the terms:
x + -1x2 + 6x3 = 0

Solving
x + -1x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -1x + 6x2) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + -1x + 6x2)' equal to zero and attempt to solve:

Simplifying
1 + -1x + 6x2 = 0

Solving
1 + -1x + 6x2 = 0

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

Divide each side by '6'.
0.1666666667 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -0.1666666667x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -0.1666666667x + x2 = 0 + -0.1666666667
-0.1666666667x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-0.1666666667x + x2 = -0.1666666667

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = -0.1666666667 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = -0.1666666667 + 0.006944444447

Combine like terms: -0.1666666667 + 0.006944444447 = -0.159722222253
0.006944444447 + -0.1666666667x + x2 = -0.159722222253

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = -0.159722222253

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}