Answer
$(-\infty,-\frac{3}{2})\cup(0,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $x(2x+3)\gt0$; the boundary points are $x=-\frac{3}{2},0$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)..(-\frac{3}{2})...(-)...(0)...(+)...$
TGhus the solutions are $x\lt -\frac{3}{2}$, plus $x\gt0$.
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 $(-\infty,-\frac{3}{2})\cup(0,\infty)$
