(3x^2-2x+1)(3x^2-2x-7)=0

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(3x^2-2x+1)(3x^2-2x-7)=0

(3x^2-2x+1)(3x^2-2x-7)=0
(3x^2-2x+1)(3x^2-2x-7)=0

(3x^2-2x+1)(3x^2-2x-7)=0
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

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