$(x-a)(x-b)(x-c)(x-d)=ex$ We can verify that $x=125,162,343$ are the roots of equation $(x-105)(x-210)(x-315)=2584x$.
My question is,Could you find five positive integers $a,b,c,d,e$, which $(x-a)(x-b)(x-c)(x-d)=ex$ has four positive integer roots?
Thanks in advance.

Thank you for your attention, some one has offered me some examples:
$(x-5)(x-6)(x-16)(x-18)=84x,x=4,9,12,20;$
$(x-3)(x-4)(x-16)(x-22)=280x,x=2,8,11,24;$
$(x-3)(x-6)(x-32)(x-44)=2520x,x=2,11,24,48.$
