Let's simplify the left side of the equation step by step:

200(2(2(x-1)-1)-1)
First, distribute the 2 inside the inner parentheses:
200(2(2x-2) -1) - 1

Next, distribute the 2 outside the parentheses:
200(4x - 4) - 1

Now multiply 200 by each term inside the parentheses:
800x - 800 - 1

Combine like terms:
800x - 801

Now our equation is:
800x - 801 = -600

Add 801 to both sides to isolate the variable term:
800x = 201

Finally, divide by 800 to solve for x:
x = 201/800 = 0.25125

So, the solution to the equation is x = 0.25125