(x+2)(x-3)2>0

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

1. Identify the critical points: Set each factor equal to zero to find the points where the expression changes sign.

   \[ x + 2 = 0 \quad \Rightarrow \quad x = -2 \] \[ (x - 3)^2 = 0 \quad \Rightarrow \quad x = 3 \]

   The critical points are \(x = -2\) and \(x = 3\).

2. Determine the sign of the expression in the intervals defined by the critical points: The critical points divide the number line into the following intervals:

   • \((- \infty, -2)\)
   • \((-2, 3)\)
   • \((3, \infty)\)

3. Test a point from each interval:

   • Interval \((- \infty, -2)\): Choose \(x = -3\):

     \[ (-3 + 2)(-3 - 3)^2 = (-1)(-6)^2 = (-1)(36) = -36 \quad (\text{negative}) \]

   • Interval \((-2, 3)\): Choose \(x = 0\):

     \[ (0 + 2)(0 - 3)^2 = (2)(-3)^2 = (2)(9) = 18 \quad (\text{positive}) \]

   • Interval \((3, \infty)\): Choose \(x = 4\):

     \[ (4 + 2)(4 - 3)^2 = (6)(1)^2 = (6)(1) = 6 \quad (\text{positive}) \]

4. Compile the results: The expression is positive in the intervals:

   • \((-2, 3)\)
   • \((3, \infty)\)

5. Consider the critical points:

   • At \(x = -2\), \((x + 2) = 0\), thus the expression equals zero (not included in the solution).
   • At \(x = 3\), \((x - 3)^2 = 0\), thus the expression also equals zero (not included in the solution).

6. Conclusion: The solution to the inequality \((x + 2)(x - 3)^2 > 0\) is:

\[ \boxed{(-2, 3) \cup (3, \infty)} \]