Prove that $\mathfrak{sl}(3, F)$ modulo $Z(\mathfrak{sl}(3,F)$ is semisimple

Question

Let $L= \mathfrak{sl}(3, F)$, with $charF= 3$. I want to prove that $L/Z(L)$ is semisimple. I already know that $Z(L)$ is the set of scalar matrices in $L$. I think it is sufficient to show that every solvable ideal, or equivalently, the radical lies in $Z(L)$, but I don’t know how to move on from here. Any hints?