由(3x^2-2x+1)(3x^2-2x-7)+12=0得(3x^2-2x+1)(3x^2-2x+1-8）+12=0
有(3x^2-2x+1)^2-8(3x^2-2x+1)+12=0
即(3x^2-2x+1-6）(3x^2-2x+1-2）=0
即有3x^2-2x-5=0或者3x^2-2x-1=0,可解得x=5/3或x=-1或x=-1/3或x=1
经检验,所有根均为原方程的解,故可得x=5/3或x=-1或x=-1/3或x=1