Transcendental equations involving more than 2 terms
Solution 1:
Burniston and Siewert built a solution for the equation:
$$ze^z=a(z+b)$$
through an integral representation.
== References ==
[68] C. E. Siewert and E. E. Burniston, "Solutions of the Equation $ze^z=a(z+b)$," Journal of Mathematical Analysis and Applications, 46 (1974) 329-337.
http://www4.ncsu.edu/~ces/pdfversions/68.pdf