To solve the equation \(50.3(n + 9.25) = -120.72\), we will first divide both sides by 50.3:
\[ n + 9.25 = \frac{-120.72}{50.3} \]
Now we calculate \(\frac{-120.72}{50.3}\):
\[ n + 9.25 \approx -2.4 \]
Next, we isolate \(n\) by subtracting 9.25 from both sides:
\[ n \approx -2.4 - 9.25 \]
Calculating that gives:
\[ n \approx -11.65 \]
Thus, the solution is:
\[ \boxed{-11.65} \]