Решите уравнение: (x+1)(x^2+4x+2)=2*|x+1|.

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

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

\[= - 2 \bullet (x + 1)\]

\[(x + 1)\left( x^{2} + 4x + 2 + 2 \right) = 0\]

\[(x + 1)\left( x^{2} + 4x + 4 \right) = 0\]

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

\[x = - 1 \Longrightarrow \ \ \ не\ подходит.\]

\[x = - 2.\]

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

\[= 2 \bullet (x + 1)\]

\[(x + 1)\left( x^{2} + 4x + 2 - 2 \right) = 0\]

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

\[x = - 1\]

\[x = - 4 \Longrightarrow \ \ \ не\ подходит.\]

\[Ответ:\ - 2;\ - 1;0.\]