Determine the Value of Consecutive Integers' Product

Consider three consecutive integers represented as $n$, $n+1$, and $n+2$. If the product of these integers is expressed as $P = n(n+1)(n+2)$, and this product is equal to 240, what is the value of $n$?

Find the value of $n$ that satisfies the equation $n(n+1)(n+2) = 240$.