IrMO 2019 Problem 4

Find the set of all quadruplets $(x,y, z,w)$ of non-zero real numbers which satisfy $$1 +\frac{1}{x}+\frac{2(x + 1)}{xy}+\frac{3(x + 1)(y + 2)}{xyz}+\frac{4(x + 1)(y + 2)(z + 3)}{xyzw}= 0$$