I am trying to solve for $N_{mpn}$. Can this be solved? $$\sum_{i=1}^K\frac{V_id_iP_i}{1-e^{-V_id_iN_{mpn}}}=\sum_{i=1}^KV_id_in_i$$
In researching this, it did not appear that I could pull any constants out because every variable is part of the iteration. I do know that each side needs to be simplified in order to remove the summations, but I couldn't find a resource that could succinctly tell me how to simplify a summation that contained multiple variables, each one being directly iterated in the summation.
For example, I know that: $$\sum_{i=1}^N6yx_i=6y\sum_{i=1}^Nx_i$$
But it's not clear to me how to simplify something like: $$\sum_{i=1}^Ny_ix_iz_i$$
Let alone something like the left side of the equation. Frankly, I don't know where to start.