To find the zeroes, which are the x-intercepts, it's where y = 0. To solve nonlinear equations, a good method is to make use of the Null Factor Law, which states that if two things multiply to give 0, then at least one of those things must be 0.
So in your case, you have . You have three things multiplying to give 0, namely 3, (x - 5) and (x - 17), so that means either x - 5 = 0 or x - 17 = 0 (as obviously 3 is not 0). Therefore x = 5 or x = 17.