The given expression can be simplified as follows:

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

So, the expression simplifies to:

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

Now, set each factor to zero:

|x|-x=0
If x is positive, then |x|=x. So, x-x=0, which gives x=0.
If x is negative, then |x|=-x. So, -x-x=0, which gives x=0.
Therefore, x=0.

x+1=0
This gives x=-1.

So, the solutions are x=0 and x=-1.