Решите уравнение: (3x^2-6x+2)(x^2-2x-1)-5x^2+10x-7=0.

\[t = x^{2} - 2x - 1\]

\[(3t + 5)t - (5t + 12) = 0\]

\[3t^{2} - 12 = 0\]

\[3 \bullet \left( t^{2} - 4 \right) = 0\]

\[(t - 2)(t + 2) = 0\]

\[1)\ x^{2} - 2x - 1 = 2\]

\[x² - 2x - 3 = 0\]

\[D = ( - 2)^{2} - 4 \cdot 1 \cdot ( - 3) =\]

\[= 4 + 12 = 16\]

\[x_{1} = \frac{2 + \sqrt{16}}{2} = \frac{2 + 4}{2} = \frac{6}{2} = 3\]

\[x_{2} = \frac{2 - \sqrt{16}}{2} = \frac{2 - 4}{2} = \frac{- 2}{2} =\]

\[= - 1\]

\[2)\ x^{2} - 2x - 1 = - 2\]

\[x^{2} - 2x + 1 = 0\]

\[(x - 1)^{2} = 0\]

\[x - 1 = 0\]

\[x = 1\]

\[Ответ:3;\ - 1;1.\]