2. A function $f(x)$ satisfies
$$
(2-x) f(x)-2 f(3-x)=-x^{3}+5 x-18
$$
for all real numbers $x$. Solve for $f(0)$.
Answer: $f(0)=7$
Solution: Set $x=0$ and $x=3$ to obtain the system
$$
\left\{\begin{array}{ll}
2 f(0)-2 f(3) & =-18 \\
-f(3)-2 f(0) & =-30
\end{array}\right.
$$

We can solve for $f(0)$ from the system and obtain $f(0)=7$.