Решите уравнение (2x+5)(x−6)+2(3x+2)(3x−2)=5(2x+1)^2+11.

Ответ:

\[(2x + 5)(x - 6) + 2(3x + 2)(3x - 2) = 5(2x + 1)^{2} + 11\]

\[2x^{2} - 12x + 5x - 30 + 2\left( 9x^{2} - 4 \right) = 5\left( 4x^{2} + 4x + 1 \right) + 11\]

\[2x^{2} - 7x - 30 + 18x^{2} - 8 = 20x^{2} + 20x + 5 + 11\]

\[20x^{2} - 20x^{2} - 7x - 20x = 16 + 38\]

\[- 27x = 54\]

\[x = - 2.\]

\[Ответ:x = - 2.\]