smc

Denote three roots as $r_1<r_2<r_3$. Following from Vieta's formula, $r_1{r}_2{r}_3=-6$. Case 1: All roots are negative. We have the following solution: $\left(-3,-2,-1\right)$. Case 2: One root is negative and two roots are positive. We have the following solutions: $\left(-3,1,2\right)$, $\left(-2,1,3\right)$, $\left(-1,2,3\right)$, $\left(-1,1,6\right)$. Putting all cases together, the total number of solutions is $\boxed{5}$.