To solve this equation, we will first expand both sides using the distributive property:

(x-1)(x-3) = x^2 - 3x - x + 3
= x^2 - 4x + 3

(x-2)(x-4) = x^2 - 4x - 2x + 8
= x^2 - 6x + 8

Now we can set the two expanded expressions equal to each other and solve for x:

x^2 - 4x + 3 = x^2 - 6x + 8

Now we can simplify the equation by subtracting x^2 from both sides and combining like terms:

-4x + 3 = -6x + 8
2x = 5
x = 5/2

Therefore, the solution to the given equation is x = 5/2.