10x^3-6x^2+6x=0

Solution for 10x^3-6x^2+6x=0 equation:

Simplifying
10x3 + -6x2 + 6x = 0

Reorder the terms:
6x + -6x2 + 10x3 = 0

Solving
6x + -6x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(3 + -3x + 5x2) = 0

Ignore the factor 2.
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 + -3x + 5x2)' equal to zero and attempt to solve:

Simplifying
3 + -3x + 5x2 = 0

Solving
3 + -3x + 5x2 = 0

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

Divide each side by '5'.
0.6 + -0.6x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -0.6x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -0.6x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -0.6x + x2 = 0 + -0.6
-0.6x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-0.6x + x2 = -0.6

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = -0.6 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = -0.6 + 0.09

Combine like terms: -0.6 + 0.09 = -0.51
0.09 + -0.6x + x2 = -0.51

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = -0.51

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}