In his Ars Magna Cardano specifies procedures to "depress" a cubic - a means to convert an equation such as $x^3+6x^2=100$ to $y^3=84+12y$, eliminating the $x^2$ term.
Was he the one who discovered how to do this? (Or was he just the first to publish it? (Or neither?))
In his Quesiti Tartaglia claimed to have known how to solve cubics of the form $x^3+ax^2=c$, which made me wonder if he knew how to eliminate the $x^2$ term. So far I haven't found anything definitive that indicates who first discovered the appropriate substitution.