x^3(x+1)(x-2)=0

Solution for x^3(x+1)(x-2)=0 equation:

Simplifying
x3(x + 1)(x + -2) = 0

Reorder the terms:
x3(1 + x)(x + -2) = 0

Reorder the terms:
x3(1 + x)(-2 + x) = 0

Multiply (1 + x) * (-2 + x)
x3(1(-2 + x) + x(-2 + x)) = 0
x3((-2 * 1 + x * 1) + x(-2 + x)) = 0
x3((-2 + 1x) + x(-2 + x)) = 0
x3(-2 + 1x + (-2 * x + x * x)) = 0
x3(-2 + 1x + (-2x + x2)) = 0

Combine like terms: 1x + -2x = -1x
x3(-2 + -1x + x2) = 0
(-2 * x3 + -1x * x3 + x2 * x3) = 0
(-2x3 + -1x4 + x5) = 0

Solving
-2x3 + -1x4 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-2 + -1x + x2) = 0

Factor a trinomial.
x3((-1 + -1x)(2 + -1x)) = 0

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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 = {-1, 2}