In the first major studies into the magical properties of the complex number and the application to solving the cubic equation, Cardano did the following in around 1539:
He reduced the cubic equation
to the form
where $p$ and $q$ are real numbers.
(1). How did Cardano get to this?
There was also another solution to the cubic, discovered before 1926, and it is often referred to as the (del Ferro-)Cardano solution, and is perhaps where Cardano went from in his first reduction. This solution is:
(2). How is the del Ferro-Cardano solution derived?