For which t values the two vectors are parallel to each other

Question

$\overrightarrow{r_{1}}(t)=[t+6,-3,t+2]$

$\overrightarrow{r_{2}}(t)=[-10,t+7,-2t^{2}]$

For which t values the two vectors are parallel to each other?

My try:

I tried cross product, and got : $$\left[5t^{2}-9t-14,2t^{3}+12t^{2}-10t-20,t^{2}+13t+12\right]$$

so if both vectors are parallel :

$$ \begin{cases} 5t^{2}-9t-14=0\\ 2t^{3}+12t^{2}-10t-20=0\\ t^{2}+13t+12=0 \end{cases} $$

but I don't get a solution :(

any idea?