here. the problem is different, but when you get to the step that you're on, i explain the process.
first, get all the powers of x to be the same, that is n. notice that in the middle term the power is n - 2. change all n's in that term to n + 2 (the index on the series will change also).
then, make sure your series all start at the same index. usually this is done by evaluating some terms of some series so that they catch up with others. in this case, you can just set all of them to begin at n = 0. this won't change what you have.
then combine all the series together, factor out the and set its coefficient to zero. from this you can get a recursive formula to find the coefficients of your series solution. i hope you know how to take it from there.