Solution

Given that the equation has integer solutions, the two factors \((x-18)\) and \((x+28)\) must both be integers. The product of these must be 47. Note also that the latter factor is greater than the former. This is only possible if either \((x-18)=1\) and \((x+28)=47\), or if \((x-18)=-47\) and \((x+28)=-1\). Hence the two solutions are \(x=19\) and \(x=-29\).