Apositive integer is 5 more than 23 times another. their product is 6732. find the two integers.

Another way to write this is:
x = 23y + 5
xy = 6732

Now plug in the first equation into the second:
(23y + 5)y = 6732
23y^2 + 5y - 6732 = 0

Either use quadratic equation or factor:
(y - 17)(23y + 396) = 0
y = 17 or -396/23

You know you can automatically eliminate the second y because it's negative and you need the two integers to multiply to a positive number (6732).

Plug y = 17 back into either equation (second might be easier):
17x = 6732
x = 396