I have the following inequality that I need to find all solutions of:
$2x^3-8x > 5x^2-20$
My guess is that you would have to turn this into a polynomial equation and let the right hand side equal to $0$ (i.e. $2x^3-5x^2-8x+20=0$). By using the factor theorem you could guess a solution that is a factor of $20$, then use long division to solve for the other two roots. But how would you know whether the inequality is greater than the root (i.e. $>$) or less than the root (i.e. $<$)? Is it something you just need to guess and check? Or is there another way?