Let's simplify the equation step by step:

First, simplify the innermost parentheses:
x - 3(x - 3(x - 3))
x - 3(x - 3x + 9)
x - 3x + 9x - 27
7x - 27

Next, substitute the simplified expression back into the original equation:
111 - 3(7x - 27) = 3
111 - 21x + 81 = 3
-21x + 192 = 3

Now, isolate the variable x:
-21x = -189
x = 9

Therefore, the value of x that satisfies the equation is 9.