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

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

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

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

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

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

Combine like terms: 1x + 2x = 3x
x(2 + 3x + x2) = 0
(2 * x + 3x * x + x2 * x) = 0
(2x + 3x2 + x3) = 0

Solving
2x + 3x2 + x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x((2 + x)(1 + x)) = 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 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Subproblem 3
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
Solution
x = {0, -2, -1}