Given a Lie Algebra L and the adjoint homomorphism $ad: L \rightarrow gl (L), $ if $ad\, L$ is solvable, then so is L.

We know that Ker $ ad \,L= \{x \in L \,| [x, y] = 0 \,\,\forall y \in L\} = Z(L).$ In order to use this result, one could build the quotient algebra, $L/Z(L).$ In that case, if $L/Z(L)$ is solvable then L is solvable, meaning that one has to prove that $L/Z(L)$ is solvable.

Can somebody provide some suggestion how to prove this ?