Given $(x-1)^3+3(x-1)^2-2(x-1)-4=a(x+1)^3+b(x+1)^2+c(x+1)+d$, find$(a,b,c,d)$ 
Given $(x-1)^3+3(x-1)^2-2(x-1)-4=a(x+1)^3+b(x+1)^2+c(x+1)+d$,
  find$(a,b,c,d)$

my attempt:
$$(x+1)=(x-1)\frac{(x+1)}{(x-1)}$$
but this seems useless?
I want to use synthetic division but I don't know how

In case you don't know how to solve this most elegantly, there is still the straightforward possibility by expanding both sides. The LHS is given by
$$
x^3-5x,
$$
whereas the RSH is
$$
ax^3 + (3a + b)x^2 + (3a + 2b + c)x + a + b + c + d.
$$
