To solve this equation, we need to first simplify the equation by combining like terms:

1/3x + 2/5(x-1) = 0
1/3x + 2/5x - 2/5 = 0
(5/15)x + (6/15)x - 2/5 = 0
(11/15)x - 2/5 = 0

Next, we need to get rid of the fractions by finding a common denominator. In this case, the common denominator is 15:

(11/15)x - 6/15 = 0
(11x - 6)/15 = 0

Now, we can solve for x by multiplying both sides by 15 to get rid of the denominator:

11x - 6 = 0
11x = 6
x = 6/11

Therefore, the solution to the equation 1/3x + 2/5(x-1) = 0 is x = 6/11.