MHB Proving Two Rings Are Isomorphic

[cs0978]

I seem to be having a difficult time trying to figure out how to do this problem. It's from a non-graded homework assignment. I was able to get every other problem except for this one.Let R = Z, together with the two operations:
a + b := a + b + 3 and ab := ab + 3a + 3b + 6

Let S = Z, together with the two operations:
a + b := a + b - 2 and ab := -ab + 2a + 2b - 2

Assume ordinary addition and multiplication in Z and that R and S are rings.

Prove that R is isomorphic to S.

 

[Opalg]

I seem to be having a difficult time trying to figure out how to do this problem. It's from a non-graded homework assignment. I was able to get every other problem except for this one.Let R = Z, together with the two operations:
a + b := a + b + 3 and ab := ab + 3a + 3b + 6

Let S = Z, together with the two operations:
a + b := a + b - 2 and ab := -ab + 2a + 2b - 2

Assume ordinary addition and multiplication in Z and that R and S are rings.

Prove that R is isomorphic to S.

As a start, find what the zero and unit elements are in $R$ and $S$. An isomorphism must take the zero element of $R$ to the zero element of $S$, and the same for the unit elements.