Troubles simplifying expressions



Hello there!

I'm rather new to Maxima and now am running against a wall while trying 
to solve the forward kinematics of a delta robot.
Trying to solve the three characteristic equations directly in a 
brute-force-way was simply undoable, so I had to resort to a 
step-by-step strategy with substitutions and simplifications where possible.
However, after having solved for one coordinate, I cannot get the result 
any better with the functions of Maxima that I could come up with, they 
actually show no effect whatsoever. This strikes me, since there are so 
many places, where one can obviously factor out value and named 
constants, just that factor, factorsum or ratsubst are unable to do what 
I'm intending.
I figure I'd better not be posting the example code directly in this 
email, so here goes the link to it on pastebin: http://pastebin.com/vMKmknBf
The code contains comments where I think something is going wrong.

Can anybody please give me tips or even a helping hand about improving 
on the expression of z_final?

With Kind Regards,
Michael