10 Type the correct answer in the box. Use numerals instead of words. Consider this equation. \( \frac{10 n+25}{3 n+12}=\frac{5 \pi}{\infty+4} \) How many valid solutions does the equation have? The equation has valid solution(s).

To determine the number of valid solutions for the equation \( \frac{10 n+25}{3 n+12}=\frac{5 \pi}{\infty+4} \), we first note that \(\infty\) represents a concept rather than a numerical value, implying that the right side approaches zero. The left side, however, is a rational function that can yield valid solutions. Given that we are equating a finite expression with zero, we can conclude that the left-hand side must also equal zero. To find valid solutions, we set \(10n + 25 = 0\), leading to \(n = -\frac{5}{2}\). Thus, there is one valid solution to the equation. The equation has 1 valid solution.