3x^3-5x^2+3x=0

Solution for 3x^3-5x^2+3x=0 equation:

Simplifying
3x3 + -5x2 + 3x = 0

Reorder the terms:
3x + -5x2 + 3x3 = 0

Solving
3x + -5x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + -5x + 3x2) = 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 '(3 + -5x + 3x2)' equal to zero and attempt to solve:

Simplifying
3 + -5x + 3x2 = 0

Solving
3 + -5x + 3x2 = 0

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

Divide each side by '3'.
1 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.666666667x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1.666666667x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.666666667x + x2 = 0 + -1
-1.666666667x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.666666667x + x2 = -1

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -1 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -1 + 0.6944444447

Combine like terms: -1 + 0.6944444447 = -0.3055555553
0.6944444447 + -1.666666667x + x2 = -0.3055555553

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = -0.3055555553

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}