Solve \( 5 n^{2}+16 n+3=0 \) by factoring. Enter answers separated by a comma. \( n=\square \) or \( n=\square \)

To solve the quadratic equation \( 5n^{2} + 16n + 3 = 0 \) by factoring, we first look for two numbers that multiply to \( 5 \times 3 = 15 \) and add to \( 16 \). The numbers \( 15 \) and \( 1 \) satisfy this condition! Now we can rewrite the equation as: \( 5n^{2} + 15n + 1n + 3 = 0 \). Next, we group the terms: \( (5n^{2} + 15n) + (1n + 3) = 0 \). Factoring each group gives us: \( 5n(n + 3) + 1(n + 3) = 0 \). Now we can factor out \( (n + 3) \): \( (n + 3)(5n + 1) = 0 \). Setting each factor to zero gives: \( n + 3 = 0 \) or \( 5n + 1 = 0 \). Thus, we find: \( n = -3 \) or \( n = -\frac{1}{5} \). So, the solutions are: \( n = -3, -\frac{1}{5} \)