Solve the equation \(8^x-7(4)^x+14(2)^x-8=0\), where \(x\in\mathbb{R}\).

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① Prove that \(u-1\) is a factor of \(u^3-7u^2+14u-8=0\).\n\n

② Solve the equation\n\[8^x-7(4)^x+14(2)^x-8=0\]\nwhere \(x\in\mathbb{R}\).

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