Question: Convert given Eq. into Polynomial with a variable substitution

Can someone explain how to use Maple to get from Eq. (4) to Eq. (5) using Eq. (6) to (8)?

This is the Peng Robinson Equation of State (1976)

I tried some stuff like using algsubs v=Z*R*T/p on Eq. (4) and then do some polynomial operations (expand, collect etc.) It did not work out though. I'm grateful for any advice!

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