Which of the following is the solution set for `x(x-3)(x+2)gt0`?

Options

A. `x lt -2`
B. `-2 lt x lt 3`
C. `-2 lt x lt 3 ` or `x gt 3`
D. `-2ltx lt0` or `x gt 3`

Explanation

To solve the inequality \( x(x-3)(x+2) > 0 \), we will follow these steps:

### Step 1: Find the roots of the polynomial
We start by setting the expression equal to zero to find the critical points:
\[ x(x-3)(x+2) = 0 \]
This gives us the roots:
- \( x = 0 \)
- \( x - 3 = 0 \) → \( x = 3 \)
- \( x + 2 = 0 \) → \( x = -2 \)