Answer
$ (-7,3) $
Work Step by Step
Step 1. Rewrite and factor the inequality as $x^2+4x-21\lt0 \longrightarrow (x+7)(x-3)\lt0$
Step 2. Identify the boundary points as $x=-7,3$ and the resulting three intervals $(-\infty,-7),(-7,3),(3,\infty)$
Step 3. Choose test values in each interval $x=-8,0,4$ and check the inequality, the results are $False,\ True,\ False.$
Step 4. Thus the solution interval for the inequality is $ (-7,3) $
