If (x-2)(x-3) = 0 then the points of x are 2 , 3
Let us plot these points on a number line , Now for all the points at the left of 2 , both (x-2) and (x-3) are negative , which makes (x-2)(x-3) positive .
Similarly , for points lying between 2 and 3 , (x-2) is +ve , (x-3) is -ve that makes the product -ve .
Similarly for point lying at the right of 3 , both (x-2) and (x-3) are +ve that makes the product +ve .
Now in the given expression we need the product to be greater than 0 that is +ve , so the solution is x > 3 , x < 2