Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of Algebra" using complex numbers, at a time when the concept of complex numbers was not known. However, it is also noted (in the pages of history) that Tartaglia (1535) revealed his solution to Cardano, who got it published in his name. This period of history is filled with disputes among Ferro, Tartaglia and Cardano to claim their work. This article describes a new method for solving cubic equations. The proposed method is different from the well-known Cardano's method as well as the other methods available in the literature. In this method the given (reduced) cubic equation is decomposed and its linear factor is extracted in a novel manner.