To solve this equation, we can first simplify it by expanding the square and then solve for x by isolating it on one side.

(3x-1)^2 - 2|3x-1| - 3 = 0
(3x-1)(3x-1) - 2|3x-1| - 3 = 0
(9x^2 - 6x + 1) -2*|3x-1| - 3 = 0

Now we need to consider the absolute value expression separately for positive and negative values of (3x-1).

For (3x-1) >= 0:
(9x^2 - 6x + 1) - 2*(3x-1) - 3 = 0
9x^2 - 6x + 1 - 6x + 2 - 3 = 0
9x^2 - 12x = 0
3x(3x - 4) = 0
x = 4/3, x = 0

For (3x-1) < 0:
(9x^2 - 6x + 1) - 2*(-3x+1) - 3 = 0
9x^2 - 6x + 1 + 6x - 2 - 3 = 0
9x^2 - 4 = 0
x = ±2/3

Therefore, the solutions to the equation are x = 0, x = 4/3, x = -2/3.