problem: Solve for $z$ in the following equation: $2-3iz = 3 + 2iz$.
solution: $2-3iz = 3 + 2iz \Rightarrow -1 = 5iz \Rightarrow z = \frac{-1}{5i}$. Multiplying the numerator and denominator by $-i$, we get $z = \frac{-1}{5i} \cdot \frac{-i}{-i} = \boxed{\frac{i}{5}}$.