Finding Maximum Integer Value of n for Product P

Consider a product of two integers, say $a$ and $b$, such that $a$ is five more than twice an integer $n$, and $b$ is three less than three times the same integer $n$. If the product $P = a imes b$ can be expressed as $$P = (2n + 5)(3n - 3)$$, what is the maximum integer value of $n$ such that $P$ remains a positive integer less than 1000?