∵y=6x^3-12x^2+6x+1
∴y'=18x^2-24x+6
=6(3x^2-4x+1)
令y'<0,则3x^2-4x+1<0,(-x+1)(-3x+1)<0
∴(x-1)(3x-1)<0
∴1/3<x<1
即单调减区间为(1/3,1)