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

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

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

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

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

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

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

Solving
-2x + 1x2 + x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x((-2 + -1x)(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 '(-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
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, -2, 1}