A Z'-model consists of a u(1)-extension to the SM's gauge algebra, requiring a choice of integer charges for each of the Weyl fermion in the theory. However, these charges cannot be chosen arbitrarily; they must (in general) satisfy a set of conditions called the anomaly cancellation conditions. These conditions are a set of polynomial equations in the integer charges. In this talk, I will demonstrate how these equations may be solved using simple geometric methods, thereby reducing the space of all Z'-models to a phenomenologically significant subspace. This is based on the papers: 1912.04804 and 2006.03588.