To solve this equation, we first need to expand the terms:

(1-x)^2 - x(1+x) = 0

Expanding the terms gives:

(1 - 2x + x^2) - x - x^2 = 0

Now we can simplify the equation:

1 - 2x + x^2 - x - x^2 = 0
1 - 3x = 0

Now we can solve for x:

1 - 3x = 0
3x = 1
x = 1/3

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