Answer
$(-\infty, -2)\cup(5,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{3(x+2)}{x-5}\gt0$
Step 2. Identify the boundary points $x=-2, 5$ and separate the number line into intervals $(-\infty, -2)$, $(-2,5)$, and $(5,\infty)$
Step 3. Use test points $x=-3,0,6$ to get the signs of the left side of the inequality as $+,-,+$
Step 4. Based on the signs, we have the solution as $(-\infty, -2)\cup(5,\infty)$
