We have the equation which can be factored as (2x - 5)(17x - 13) = 0.
Remember, whenever a product gives us zero, it means that at least one of those factors must be equal to zero. It's a simple consequence of the so-called zero-product property.
So, we can solve this equation by setting each factor in turn equal to zero:
Let's start with the first factor, (2x - 5):
Set (2x - 5) = 0, to get the first possible solution for x.
We can solve for x by isolating it on one side. Add 5 to both sides to obtain:
2x = 5
Now, divide both sides of the equation by 2. The solution we have for x is:
x = 5/2
Now, we're going to use the same method to solve the other factor, (17x - 13) for x:
Set (17x - 13) = 0
To isolate x, add 13 to both sides:
17x = 13
Now, divide both sides by 17 to solve for x, we have:
x = 13/17
So, the solutions to the equation (2x-5)(17x-13)=0 are x = 5/2 and x = 13/17.