Here are the steps to solve polynomial inequalities:

1. Move everything to the left hand side to  make your inequality looks like (here the inequality symbol can also be or )
2. Find the zeros of (by factoring if it is possible)
3. Plot the zeros on the number line and these zeros will divide the number line into several intervals
4. Pick a sample point on each interval and plugin it to
5. If after plugin you get is true then the interval on the number line where your belong is part of the solution, otherwise the interval is not part of the solution

The videos below will guide you step by step to solve te polynomial inequalities using a concrete example