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

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

Simplifying
0 = x4 + -2x3 + x2

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

Solving
0 = x2 + -2x3 + x4

Solving for variable 'x'.
Remove the zero:
-1x2 + 2x3 + -1x4 = x2 + -2x3 + x4 + -1x2 + 2x3 + -1x4

Reorder the terms:
-1x2 + 2x3 + -1x4 = x2 + -1x2 + -2x3 + 2x3 + x4 + -1x4

Combine like terms: x2 + -1x2 = 0
-1x2 + 2x3 + -1x4 = 0 + -2x3 + 2x3 + x4 + -1x4
-1x2 + 2x3 + -1x4 = -2x3 + 2x3 + x4 + -1x4

Combine like terms: -2x3 + 2x3 = 0
-1x2 + 2x3 + -1x4 = 0 + x4 + -1x4
-1x2 + 2x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-1x2 + 2x3 + -1x4 = 0

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

Factor a trinomial.
x2((-1 + x)(1 + -1x)) = 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 '(-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}