$3|9-2n|=-5n$

Step 1 ：Split the equation into two possible scenarios: when the expression inside the absolute value is positive, and when it is negative. Therefore, we need to solve for both cases separately.

Step 2 ：For the first case, solve the equation $27-6n=-5n$. The potential solution is $n=27$.

Step 3 ：For the second case, solve the equation $6n-27=-5n$. The potential solution is $n=\frac{27}{11}$.

Step 4 ：Check if these solutions satisfy the original conditions of the absolute value function.

Step 5 ：Neither of the potential solutions satisfy the original conditions of the absolute value function.

Step 6 ：Final Answer: The equation $3|9-2n|=-5n$ has $\boxed{{\displaystyle \text{no solutions}}}$.