Determine the sum of all possible positive integers n , the product...

$n^2-15 n-27$ is always odd number for all $n \in I$ n must be maximum of two digit number. because maximum product of three digit number is 729 \& minimum value of $n^2-15 n-27$ for 3 digits number is $10000-1500-27$ which is greater than 729 . $n^2-15 n-27$ is increasing function for all $n \in\{8,9,10, \ldots \ldots \ldots \ldots$}. at $n=17, n^2-15 n-27$ is equal to 17 at $n=19, n^2-15 n-27$ is equal to 49 at $n=21, n^2-15 n-27$ is equal to 99 And maximum product of digits of two digit number is 81 $\Rightarrow$ So n must be less than 21 $\Rightarrow$ Between 1 to $15, n^2-15 n-27$ is negative $\Rightarrow$ So $\mathrm{n}=17$ only Sum of possible number equal to 17