Actually, your equation
is a cubic equation, since the highest-order term is x³. Fortunately, we can easily factor out an overall x,
and write the quadratic term as a complete square:
How can the left-hand side be non-negative (which is what "≥0" means)?
Well, the term (x+1)² is always non-negative, because it's a square. In fact it is
positive for all x≠-1, only for x=-1 is it zero.
So the entire left-hand side of the inequality is non-negative when x is non-negative, i.e. for all x≥0, and when x=-1. In interval notation, you could write the solution set as