To solve the equation (4x-1)(5/4x-6) = 0, we can set each factor equal to zero and solve for x.

Setting 4x-1 = 0:
4x = 1
x = 1/4

Setting 5/4x-6 = 0:
5/4x = 6
5 = 24x
x = 5/24

Therefore, the solutions to the equation are x = 1/4 and x = 5/24.