I come across this type of question pretty often, and while my way of solving is correct and gives me the right answer, it’s a bit tedious and I was wondering if there is a easier method

My method:

if x=3 is one solution, then the equation must be divisible by (x-3)

The I basically do long division of x^2 + rx -24 by x -3

The remainder I get is 3r - 15

As x-3 perfectly divides the equation 3r - 15 =0

x = 5