(x+5)*(x-15)>0

To solve the inequality \((x + 5)(x - 15) > 0\), follow these steps:

1. Find the critical points: Set each factor to zero to find the values of \(x\) where the expression changes sign. \[ x + 5 = 0 \implies x = -5 \] \[ x - 15 = 0 \implies x = 15 \]

2. Determine the intervals: The critical points \(-5\) and \(15\) divide the number line into three intervals:

   • \( (-\infty, -5) \)
   • \( (-5, 15) \)
   • \( (15, \infty) \)

3. Test a point from each interval:

   • For the interval \( (-\infty, -5) \), choose \(x = -6\): \[ (-6 + 5)(-6 - 15) = (-1)(-21) = 21 > 0 \quad \text{(True)} \]

   • For the interval \( (-5, 15) \), choose \(x = 0\): \[ (0 + 5)(0 - 15) = (5)(-15) = -75 < 0 \quad \text{(False)} \]

   • For the interval \( (15, \infty) \), choose \(x = 16\): \[ (16 + 5)(16 - 15) = (21)(1) = 21 > 0 \quad \text{(True)} \]

4. Write the solution: The expression \((x + 5)(x - 15) > 0\) is true in the intervals where the tests return true:

   • The solution to the inequality is: \[ x \in (-\infty, -5) \cup (15, \infty) \]

Final answer: \(x \in (-\infty, -5) \cup (15, \infty)\)