In the depressed cubic of Scipione del Ferro the equation
x^3 + px = q substitutes x = u + v and generates the equation u^3 + v^3 + (3uv + p)(u + v) = q.
Paul Nahin asserts that this can be written as 3uv+p = 0 and thus u^3 + v^3 = q. This step is clear, but what is not clear to me is why 3uv + p = 0.
Could someone explain please.