Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 159: 39

$(-\infty,-2)U(3,\infty)$

Step 1. Factor the quadratic, we have $(x+2)(x-3)\gt0$ Step 2. The boundary points are $x=-2$ and $x=3$ Step 3. Use test points at $x=-3, 0, 4$, the signs of the quadratic are $+, -, +$ Step 4. The inequality requires positive, thus the solutions are $(-\infty,-2)U(3,\infty)$