Answer
$(-4,-3)$.
Work Step by Step
Step 1. Rewrite and factor the inequality to get $x^2+7x+12\lt0$ and $(x+4)(x+3)\lt0$
Step 2. Identify the boundary points $x=-4,3$ which separate the number line into three intervals: $(-\infty,-4),(-4,-3),(-3,\infty)$
Step 3. For each interval, choose a test value and test the inequality, use $x=-5,-3.5,0$ and we have the result as $False, True, False$.
Step 4. Thus the solution interval is $(-4,-3)$.
