When trying to find possible roots of an equation, we can start by using the rational root theorem to find all the possible real roots.  You can also use Descartes rule of signs to possibly eliminate positive or negative roots.

If you have a cubic equation you can use synthetic division to find a root, which will leave you ith coefficients to a quadratic equation.

From here you can use quadratic formula, complete the square or other methods of factoring to get the remaining roots.