Cubic equations were known since ancient times, even by the Babylonians. However, they did not know how to solve all the cubic equations. There are many mathematicians who have attempted to solve this "impossible equation". Scipione del Ferro in the 16th century made progress on the cubic by trying to understand how to solve a 3rd degree equation that lacks a 2nd degree. He passes the solution to his student, Fiore, right on his deathbed. In 1535 Niccolò Tartaglia discovered how to solve x3+px2=q and subsequently Cardano asked Tartalia for the methods. Cardano finally publishes methods for solving cubic and quartic equations. The easiest way to solve a cubic equation is to use grouping or factoring. Here is an example:Solve x3 + 12x2 − 9x − 108=0 by grouping.(x3 + 12x2) + (−9x − 108) =0 In this step, group 2 pairs of terms.x2 (x + 12) +( −9 ) (x −12)=0 Factor the common term in each group. x2 and (−9)(x+12) (x2 −9) = 0 Factor the common term again (x+12).(x+3) (x−3) (x+12)=0 Factor the difference of perfect square. The roots of this equation are −3, 3, −12. To find the cu...