First, since the LHS is an integer, we know $x$ is a multiple of $15$. Thus, let $x = 15n$. Then our equation reduces to
$$n = 3n - \left\lfloor \frac{15n}{9}\right\rfloor \implies$$
$$2n = \left\lfloor \frac{15n}{9}\right\rfloor \leq \frac{15n}{9}$$
thus ruling out any positive solutions. Now note that
$$2n = \left\lfloor \frac{15n}{9}\right\rfloor \geq \frac{15n}{9}-1 \implies$$
$$n \geq -3$$
So any possible solutions for $n$ satisfy $-3 \leq n \leq 0$. Checking manually, we see that the only solutions are $n = 0, -1, -2$, i.e. $x = 0, -15, -30$.
