Please help me with this. I really confused about the calculation

I'm trying to solve y(y+1)(y+2)(y+3) = 7920, which is a problem from my friend's kid. First I multiplied it all out:

(y^2 + y)(y + 2)(y + 3) = 7920

(y^3 + 3y^2 + 2y)(y + 3) = 7920

y^4 + 6y^3 + 11y^2 + 6y - 7920 = 0

I tried to solve it as a quadratic equation, but that didn't seem to work since this polynomial has 5 terms. I think it is 3 terms to be a trinomial.

Since this equation can't be grouped as a trinomial, I am not able to solve it by factoring. Am I on the right track? I haven't done any maths for more than 3 years, and I think I forgot almost everything I learned!

Can you please give me a hint?