\({\left( {x + 1} \right)^2}\left( {x-4} \right) = -6\left( {x + 1} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\left( {x + 1} \right)^2}\left( {x-4} \right) + 6\left( {x + 1} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 1} \right)\left( {\left( {x + 1} \right)\left( {x-4} \right) + 6} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 1} \right)\left( {{x^2}-3x + 2} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x + 1 = 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\\{{x^2}-3x + 2 = 0}\end{array}} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = -1,}\\{x = 1,\,\,}\\{x = 2.\,\,}\end{array}} \right.\)
Ответ: –1; 1; 2.