If the equation has  x2-4x-(3k-1)|x−2|−2k+8=0,k∈R has exactly three distinct solutions, then k is equal to _____.

x2-4x-(3k-1)|x−2|−2k+8=0,   k∈R (x-2)2-(3k-1)|x−2|−2k+4=0 t2-(3k-1)t-2k+4=0  where t=x-2 For exactly 3 distinct solutions, one of the roots is zero and other root is positive. k=2