A polynomial is the dot product of the normal to a plane and a space curve.
Wherever the curve intersects the plane there is a solution.
The plane intersects the axes at different points, and the lines adjoining
two intercepts form a basis. With the bases we can construct the position
where the curve intersects the plane and therefore arrive at the solutions.
This starts out finding 7th degree roots, starts a Geometric Series and then
changes to finding the roots to the 6th degree. Finally I took a stab at