Question

Quick question about series...

How would you go from:

\[\sum_{k=0}^{\inf}2(k+2)(k+1)c _{k+2}x ^{k}+\sum_{k=1}^{\inf}k c_{k}x ^{k}+\sum_{k=0}^{\inf}c _{k}x ^{k} \]

to

4c _{2} + c _{0} + sum_{k=1}^{inf}[2(k+2)(k+1)c _{k+2}+kc _{k}+c _{k}]x ^{k}

I know we factored out the constant but 4c2 + c0 doesn't make too much sense to me. any help?