To solve this equation, we need to expand and simplify the expression on the left side of the equation:

3(x-5)^2 = 3(x-5)(x-5) = 3(x^2 - 10x + 25) = 3x^2 - 30x + 75

Now, we set the expression equal to zero and simplify:

3x^2 - 30x + 75 = 0

Next, we factor out a common factor of 3:

3(x^2 - 10x + 25) = 0

Now we have a perfect square trinomial that can be factored:

3(x-5)^2 = 0

Now, we set each factor equal to zero and solve for x:

x-5 = 0
x = 5

Therefore, the solution to the equation 3*(x-5)^2 = 0 is x = 5.