Solve \( 6 n^{2}-11 n+5=0 \) by factoring. Enter answers separated by a comma. \( n=\square \) or \( n=\square \)

To factor the quadratic equation \( 6 n^{2}-11 n+5=0 \), we look for two numbers that multiply to \( 6 \times 5 = 30 \) and add up to \(-11\). The numbers \(-6\) and \(-5\) fit the bill perfectly. We can rewrite the middle term: \[ 6n^2 - 6n - 5n + 5 = 0 \] Next, group the terms: \[ (6n^2 - 6n) + (-5n + 5) = 0 \] Factoring out the common terms: \[ 6n(n - 1) - 5(n - 1) = 0 \] Now, factor by grouping: \[ (6n - 5)(n - 1) = 0 \] Setting each factor to zero gives us: 1. \( 6n - 5 = 0 \) → \( n = \frac{5}{6} \) 2. \( n - 1 = 0 \) → \( n = 1 \) Thus, the solutions are: \( n = \frac{5}{6}, 1 \)