Answer
$(-\infty,-2)\cup(-1,2)$.
See graph.
Work Step by Step
Step 1. $x^3+x^2\lt 4x+4 \Longrightarrow x^2(x+1)-4(x+1)\lt 0 \Longrightarrow (x+1)(x+2)(x-2)\lt 0$, identify boundary points $x=-2,-1,2$.
Step 2. Form intervals $(-\infty,-2),(-2,-1),(-1,2),(2,\infty)$.
Step 3. Choose test values for each interval $x=-3,-1.5,0,3$.
Step 4. Test the inequality to get results $True,\ False,\ True,\ False$.
Step 5. Thus we have the solution $(-\infty,-2)\cup(-1,2)$.
Step 6. See graph.
