Решите уравнение (2x−7)(x+1)+3(4x−1)(4x+1)=2(5x−2)^2−53.

Ответ:

\[(2x - 7)(x + 1) + 3(4x - 1)(4x + 1) = 2(5x - 2)^{2} - 53\]

\[2x^{2} - 7x + 2x - 7 + 3\left( 16x^{2} - 1 \right) = 2\left( 25x^{2} - 20x + 4 \right) - 53\]

\[2x^{2} - 5x - 7 + 48x^{2} - 3 = 50x^{2} - 40x + 8 - 53\]

\[50x^{2} - 50x^{2} - 5x + 40x = - 45 + 10\]

\[35x = - 35\]

\[x = - 1\]

\[Ответ:x = - 1.\]