\({\left( {x + 7} \right)^3} = 49\left( {x + 7} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\left( {x + 7} \right)^3}-49\left( {x + 7} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 7} \right)\left( {{{\left( {x + 7} \right)}^2}-{7^2}} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 7} \right)\left( {x + 7-7} \right)\left( {x + 7 + 7} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,x\left( {x + 7} \right)\left( {x + 14} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,\,\,\,\,\,\,}\\{x + 7 = 0,}\\{x + 14 = 0}\end{array}} \right.\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,\,\,\,\,}\\{x = -7,\,\,\,}\\{x = -14.}\end{array}} \right.\)
Ответ: –14; –7; 0.