Answer
$(-\frac{2}{3},\frac{5}{2})$
Work Step by Step
Step 1. Rewrite and factor the inequality to get $6x^2-11x-10\lt0\longrightarrow (3x+2)(2x-5)\lt0$
Step 2. Identify the boundary points $x=-\frac{2}{3}, \frac{5}{2}$ and separate the number line into three intervals $(-\infty, -\frac{2}{3})$, $(-\frac{2}{3},\frac{5}{2})$ and $(\frac{5}{2},\infty)$
Step 3. Use test points $x=-1,0,3$ to get the signs of the left side of the inequality as $+,-,+$
Step 4. Based on the signs, we have the solution as $(-\frac{2}{3},\frac{5}{2})$
