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

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

Simplifying
0 = x3 + -2x2 + x

Reorder the terms:
0 = x + -2x2 + x3

Solving
0 = x + -2x2 + x3

Solving for variable 'x'.
Remove the zero:
-1x + 2x2 + -1x3 = x + -2x2 + x3 + -1x + 2x2 + -1x3

Reorder the terms:
-1x + 2x2 + -1x3 = x + -1x + -2x2 + 2x2 + x3 + -1x3

Combine like terms: x + -1x = 0
-1x + 2x2 + -1x3 = 0 + -2x2 + 2x2 + x3 + -1x3
-1x + 2x2 + -1x3 = -2x2 + 2x2 + x3 + -1x3

Combine like terms: -2x2 + 2x2 = 0
-1x + 2x2 + -1x3 = 0 + x3 + -1x3
-1x + 2x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-1x + 2x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 2x + -1x2) = 0

Factor a trinomial.
x((-1 + x)(1 + -1x)) = 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 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 1, 1}