I don't get how you would do this

All negative x satisfy the inequality, so the solution is (-infty,0).

Either the (x-2)^2  or the (x+1)  needs to be negative (but not both) for this equation to be true

    However, (x-2)^2  is always POSITIVE (or zero)

      so the (x+1) portion must be negative

            (x+1) <0

              x <-1

(-inf, -1)

Disregard this answer.....  I didn't see the leading 'x' of the equation !!!!!

This is my answer:

(x+2)^2 is always positive or zero, so it cannot make the answer <0

so either x+1   or x   (but not BOTH) has to be less than zero for this equation to be true

x<0       or     x+1<0

x<0       or     x<-1           <======    so the only interval ONE of these is less than zero is   (-1,0)