jmc

By the distance formula, the distance between the origin and $(3\sqrt{5},d+3)$ is $\sqrt{(3\sqrt{5}{)}^2+(d+3{)}^2}$. Setting this equal to $3d$, we have $$\begin{array}{rl}9d^2& =(3\sqrt{5}{)}^2+(d+3{)}^2\\ 9d^2& =45+d^2+6d+9\\ 8d^2-6d-54& =0\\ 4d^2-3d-27& =0\\ (4d+9)(d-3)& =0\end{array}$$Thus, the values of $d$ are $-\frac{9}{4}$ and $3$. We find that $-\frac{9}{4}$ is an extraneous answer (since distance cannot be negative), so our answer is $d=\boxed{3}$.