I have the following equation (which is an adaptation of the Beattie-Bridgeman Equation of State):
$$ P = \frac{RT}{V} + \frac{B}{V^2} + \frac{C}{V^3} + \frac{D}{V^4} $$
This is a function of the form $P = f(V)$ as R, T, B, C and D are all constant with respect to P and V.
From this, my ultimate goal is to derive an equation for $dV/dP$. My first step is therefore to write the equation explicit in V, however I get stuck at:
$$ PV^4 - RTV^3 - BV^2 - CV - D = 0 $$
What steps am I missing in order to be able to write this in the form $V = f(P)$?