smc

Since this is a quartic equation, there are going to be $4$ solutions. By Vieta's formulas, since the $x^3$ term is $0$, the sum of the roots is also $0$. Therefore, the 4th root of this polynomial is $-6$. Lastly, by Vieta's Formulas, $a+c=-(1\cdot 2+1\cdot 3+1\cdot -6+2\cdot 3+2\cdot -6+3\cdot -6)+1\cdot 2\cdot 3\cdot -6=-25-36=-61=\boxed{-61}$