How do I find the zeros of a polynomial?

The equation: y = (x+5) (-2x^3-5x^2)

Your first zero is - 5 (you get this from looking at x+5) then you can just punch it into your graphing calculator and it'll give you the two other zeros: - 2/5 and 0

the reason you get these two zeros is because - 2x^3-5x^2 turns into 2/5x^3 - x^2

the x^2 is of multiplicity 2 so it'll 'bounce' off the graph at 0 like in the photo I've included