Chapter 6.3, Problem 39MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connect ions clearly and succinctly, and of uncovering pattern and structure.

Vertex z. A drawign of a planar graph has V vertices, E edges, and F regions. Suppose you know a number z such that $V=z^3-6z^2+6.E=z^3-5z^2+20,$ and $F=2z^2-5z+8.$

Find the number of vertices, edges, and regions in your graph drawing.