I think q switches sign. Either x^3+n=mx or x^3=mx+n. p has to be negative, because the two smallest of u,v,w have to be the same sign and the other opposite. So the smallest product is positive, the other two negative. But q can go either way.

Antidisirregardless, I seem to be getting complex intermediate results, as advertised. I suppose that means that the geometrical construction can't be physically realized in the 3 real root case?

So what, we wonders, did Tartaglia do? Not solve such terrible equations?