Answer
$(-2,0)$
Work Step by Step
Step 1. Rewrite the inequality as $x(x+2)\lt0$; the boundary points are $x=-2,0$
Step 2. Using test points to examine signs across the boundary points, we have $...(+)..(-2)...(-)...(0)...(+)...$; thus the solutions are $-2\lt x\lt 0$
Step 3. We can express the solutions on a real number line as shown in the figure.
Step 4. We can express the solutions in interval notation as $(-2,0)$
