Is it compulsory to solve the L.H.S. first so that it is equal to the R.H.S.?

It depends, if you can solve RHS and show that it is equal to the LHS (without solving it), then you don't need to solve LHS. 

 

However, usually, in some questions it is not intutive as to how, LHS and RHS would be equal, so you can start solving both the sides and if they both are equal to a common expression, then you can show that they are also equal to each other.