Question: Solving Power extensions


I need help with solving an equation. I have the following equation:


to this equation I applied the comand: series(%,xi) and as a result obtained:


My question is: the way to solve this equation in the manner I need is setting the coefficients in front of xi^n equal to zero for example:

24*b[0]-24*b[1] = 0 and solving for either b[1] or b[2] or

144*b[2]+12*P[cl]*L^2 = 0 and solving for P[cl].

I would like to know there is a way to do this other than pulling the expresions by hand setting them to zero and solving. 


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