Answer
$(-\infty, 1] \cup [2, 3]$
Work Step by Step
Subtract $6x^2+6$ to both sides of the inequality to obtain:
$x^3+11x-6x^2-6\le 0
\\x^3-6x^2+11x-6\le0$
Graph the function $y=x^3-6x^2+11x-6$
(refer to the attached image below for the graph)
The solution to the given inequality is the set of x-values for which $y\le0$.
Notice that $y \le 0$ in the following intervals:
$(-\infty, 1]$ and $[2, 3]$
