The roots of the equation (x−1)2−4|x−1|+3=0

The given equation can be written as |x−1|2−4|x−1|+3=0⇒(|x−1|−3)(|x−1|−1)=0 if  |x−1|−3=0⇒x−1=±3⇒x=−2  or  4 f  |x−1|−1=0⇒x−1=±1⇒x=0  or   2 The four roots are –2,0,2,4  and are in A.P