3. For which real numbers $m$ does the equation $3 x+9=m(m-x)$ have a unique solution?

(8)
Solution. By rearranging we get $(m+3) x=m^{2}-9$.

For $m \neq-3$, $m+3 \neq 0$ so there is a unique solution $x=m-3$.

(for a complete solution 8 points)

(for the solution $x=m-3$ (always), 0 points)