x(x+2)(x+3)=0

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

Simplifying
x(x + 2)(x + 3) = 0

Reorder the terms:
x(2 + x)(x + 3) = 0

Reorder the terms:
x(2 + x)(3 + x) = 0

Multiply (2 + x) * (3 + x)
x(2(3 + x) + x(3 + x)) = 0
x((3 * 2 + x * 2) + x(3 + x)) = 0
x((6 + 2x) + x(3 + x)) = 0
x(6 + 2x + (3 * x + x * x)) = 0
x(6 + 2x + (3x + x2)) = 0

Combine like terms: 2x + 3x = 5x
x(6 + 5x + x2) = 0
(6 * x + 5x * x + x2 * x) = 0
(6x + 5x2 + x3) = 0

Solving
6x + 5x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + 5x + x2) = 0

Factor a trinomial.
x((3 + x)(2 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

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