How to effectively find a starting point solving a non-linear equation?

I have the following equation (the Kurz-Giovanola-Trivedi model [1])
$$
v^2 frac{pi^2 Gamma}{P^2 D^2} + v frac{mC_0(1-k)xi}{D[1-(1-k)Iv(P)]} + G = 0,
$$
where $Iv(P)=P cdot exp(P) cdot E(P)$, $P=frac{Rv}{2D}$, $E(P)=int_{P}^{infty} frac{exp(-x)}{x} dx$ is the exponential integral function, $xi=1-frac{2k}{[1+(frac{2pi}{P})^2]^{frac{1}{2}}-1+2k}$, $v$ and $R$ are unknowns, and everything else is constant.
To solve this equation, I use MATLAB (the core function is fzero) and suppose that $v$ is an array within a range $(10^{-2};10^2)$. The fzero function attempts to find a zero of one equation with one variable and might be called with either a one-element starting point or a two-element vector (starting interval).

My question is: how to effectively find a starting point?

I have started by solving this equation relative to $P$, and it was relatively easy to determine starting points $P_0$ for different intervals of the $v$ array by trial-and-error method. After finding $P$, it was easy to find $R$.

However, now I need to solve the equation relative to $R$ directly, without the $P$-step. The trial-and-error method is not the best option here, probably due to the type of the $R(v)$-dependence (please see below).