Solve `x(x+2)^2(x-1)^5(2x-3)(x-3)^4geq0.`

Explanation

To solve the inequality \( x(x+2)^2(x-1)^5(2x-3)(x-3)^4 \geq 0 \), we will follow these steps:

### Step 1: Identify the roots of the equation
We need to find the values of \( x \) for which the expression equals zero. The expression is zero when any of its factors are zero.

1. **From \( x = 0 \)**: This gives us a root at \( x = 0 \).
2. **From \( (x + 2)^2 = 0 \)**: This gives us a double root at \( x = -2 \).
3. **From \( (x - 1)^5 = 0 \)**: This gives us a root at \( x = 1 \).
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