Solve the inequality `(x+3)(3x-2)^5(7-x)^3(5x+8)^2 >= 0.`

Explanation

To solve the inequality \((x+3)(3x-2)^5(7-x)^3(5x+8)^2 \geq 0\), we will follow these steps:

### Step 1: Identify the critical points
We first need to find the values of \(x\) that make each factor equal to zero. These critical points will help us determine the intervals to test.

- From \(x + 3 = 0\), we get \(x = -3\).
- From \(3x - 2 = 0\), we get \(x = \frac{2}{3}\).
- From \(7 - x = 0\), we get \(x = 7\).
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