Solve for \( n \). \[ K=\frac{a}{b(c+n)} \]

To solve for \( n \) in the equation \( K = \frac{a}{b(c+n)} \), we start by manipulating the equation step-by-step. First, multiply both sides by \( b(c+n) \) to eliminate the fraction: \[ K \cdot b(c+n) = a \] This simplifies to: \[ Kb(c+n) = a \] Next, divide both sides by \( Kb \) to isolate \( c+n \): \[ c+n = \frac{a}{Kb} \] Now, subtract \( c \) from both sides to solve for \( n \): \[ n = \frac{a}{Kb} - c \] Thus, the solution for \( n \) is: \[ \boxed{n = \frac{a}{Kb} - c} \]