1) Are you certain you have written it correctly? It seems there may be an extra 'z' in the middle, there.
2) Solve for singularities. With that extra 'z' gone, I get z = -3 and z = 2i. Is that what you get?
3) Having established singularities, you get to decide what region to work with. You have one selected for you. That is good. Using the central region, one of your singularities is not really a singularity. Well. it still ist, we just don't care for the moment.
4) The partial fraction decomposition will then help you on your way. I get the delightfully straightforward: