First, let's simplify the expression:

(√5-2)(3√5-2)
= 3√5(√5) - 2(√5) - 6√5 + 4
= 3(5) - 2(√5) - 6(√5) + 4
= 15 - 2√5 - 6√5 + 4
= 19 - 8√5

Next, let's evaluate the second part of the expression:

(√43)^0
= 1

So, the final answer is 19 - 8√5 + 1 = 20 - 8√5.