4x^2+8xy+3y^2-6x-7y+2
=(2x+3y)(2x+y)-2x-4x-y-6y+2
=(2x+3y)(2x+y)-(2x+y)-4x-6y+2
=(2x+y)(2x+3y-1)-2(2x+3y-1)
=(2x+y-2)(2x+3y-1)