To solve this equation, we first need to simplify the expression inside the parentheses:

(3 1/2 + (2/3))^2 = (7/2 + 2/3)^2
= (21/6 + 4/6)^2
= (25/6)^2
= 625/36

Now we can rewrite the equation using the simplified expression:

(625/36) * x + 3/18 = 5/18

Next, we can simplify the equation by multiplying both sides by 18 to get rid of the fractions:

625x/36 + 3 = 5

Now, we can move 3 to the other side of the equation:

625x/36 = 5 - 3
625x/36 = 2

To solve for x, we can multiply both sides by 36/625:

x = 2 * 36/625
x = 72/625

Therefore, the solution to the equation is x = 72/625.