Решите уравнение: (x-2)(x^2+8x+16)=7(x+4).

\[(x - 2)\left( x^{2} + 8x + 16 \right) = 7(x + 4)\]

\[(x - 2)(x + 4)^{2} - 7(x + 4) = 0\]

\[(x + 4)\left( (x - 2)(x + 4) - 7 \right) = 0\]

\[(x + 4)\left( x^{2} - 2x + 4x - 8 - 7 \right) = 0\]

\[(x + 4)\left( x^{2} + 2x - 15 \right) = 0\]

\[1)\ x + 4 = 0\]

\[x = - 4.\]

\[2)\ x^{2} + 2x - 15 = 0\]

\[D_{1} = 1 + 15 = 16.\]

\[x_{1} = - 1 + 4 = 3;\]

\[x_{2} = - 1 - 4 = - 5.\]

\[Ответ:x = - 5;\ \ x = 3.\]