Solve the equation and check the result. (If there is no solution, enter NO SOLUTION. \[ \frac{n}{56}-\frac{n}{7}=\frac{9 n}{8} \]

To solve the equation \[ \frac{n}{56} - \frac{n}{7} = \frac{9n}{8}, \] we start by finding a common denominator for the fractions. The least common multiple of 56, 7, and 8 is 112. Now, we rewrite each term with this common denominator: \[ \frac{n}{56} = \frac{2n}{112}, \quad \frac{n}{7} = \frac{16n}{112}, \quad \frac{9n}{8} = \frac{126n}{112}. \] Substituting these into the equation gives us: \[ \frac{2n}{112} - \frac{16n}{112} = \frac{126n}{112}. \] Combining the left side: \[ \frac{2n - 16n}{112} = \frac{126n}{112}, \] which simplifies to: \[ \frac{-14n}{112} = \frac{126n}{112}. \] Multiplying through by 112 to eliminate the denominators: \[ -14n = 126n. \] Now, we can add \(14n\) to both sides: \[ 0 = 140n. \] To solve for \(n\), divide both sides by 140: \[ n = 0. \] Now, let's check the solution by substituting \(n = 0\) back into the original equation: \[ \frac{0}{56} - \frac{0}{7} = \frac{9 \times 0}{8}. \] Simplifying both sides gives: \[ 0 - 0 = 0, \] which is true. Thus, the solution is valid. The solution to the equation is \[ \boxed{0}. \]