Solve the following inequality.

To solve the inequality , we first rearrange it to set everything to one side:

Next, we can attempt to find the roots of the polynomial by using either synthetic division or the Rational Root Theorem. Testing potential rational roots, we find that is a root:

Thus, we can factor the polynomial as

Now, we can find the roots of using the quadratic formula:

This gives us the roots:

Thus, the complete factorization is:

Now we need to find the intervals where

The critical points are and . We test the intervals , , , :

Hence, this means the solution intervals are:

The inequality includes the endpoints where it equals , so the final solution is