Решите уравнение: (x-2)^2-2(x+1)^2=(3-x)(3+x).

\[(x - 2)^{2} - 2(x + 1)^{2} = (3 - x)(3 + x)\]

\[x^{2} - 4x + 4 - 2\left( x^{2} + 2x + 1 \right) = 9 - x^{2}\]

\[2x^{2} - 4x - 5 - 2x^{2} - 4x - 2 = 0\]

\[- 8x = 7\]

\[x = - \frac{7}{8}.\]