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

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

Simplifying
0 = -1x4 + 3x3 + -2x2

Reorder the terms:
0 = -2x2 + 3x3 + -1x4

Solving
0 = -2x2 + 3x3 + -1x4

Solving for variable 'x'.
Remove the zero:
2x2 + -3x3 + x4 = -2x2 + 3x3 + -1x4 + 2x2 + -3x3 + x4

Reorder the terms:
2x2 + -3x3 + x4 = -2x2 + 2x2 + 3x3 + -3x3 + -1x4 + x4

Combine like terms: -2x2 + 2x2 = 0
2x2 + -3x3 + x4 = 0 + 3x3 + -3x3 + -1x4 + x4
2x2 + -3x3 + x4 = 3x3 + -3x3 + -1x4 + x4

Combine like terms: 3x3 + -3x3 = 0
2x2 + -3x3 + x4 = 0 + -1x4 + x4
2x2 + -3x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
2x2 + -3x3 + x4 = 0

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

Factor a trinomial.
x2((1 + -1x)(2 + -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 + -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
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 1, 2}