Find the solution of the following polynomial inequality. Express your answer in interval notation.
\[
x(x+2)(x-3) \leq 0
\]

Step 1 ：We are given the polynomial inequality \(x(x+2)(x-3) \leq 0\).

Step 2 ：The inequality will be satisfied when the product is less than or equal to zero. This happens when either all three factors are positive, or one or two of them are negative.

Step 3 ：We find the roots of the equation \(x(x+2)(x-3) = 0\), which are \(x = 0\), \(x = -2\), and \(x = 3\).

Step 4 ：These roots divide the number line into four intervals: \((-∞, -2)\), \((-2, 0)\), \((0, 3)\), and \((3, ∞)\).

Step 5 ：We test a number from each interval in the inequality to see if it is satisfied.

Step 6 ：The solution to the inequality is the union of the intervals \((-∞, -2]\) and \([0, 3]\). This means that the inequality is satisfied for all x in these intervals.

Step 7 ：Final Answer: \(\boxed{(-\infty, -2] \cup [0, 3]}\)