Demonstration of the Importance of Factoring in Solving a Fundamental Equation Involving the Riemann Zeta Function

The author presents a simple approach which can be used to tackle various special cases of some well-known problems involving zeta functions. A self-contained argument, which requires only basic prerequisite mathematical knowledge, is used to furnish a new proof of a result involving the Riemann zeta function which can help in settling more general conjectures.