\(\left( {x + 3} \right)\left( {x + 1} \right)\left( {x-7} \right) = \left( {x + 3} \right)\left( {x + 1} \right)\left( {x-8} \right)\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 3} \right)\left( {x + 1} \right)\left( {x-7} \right)-\left( {x + 3} \right)\left( {x + 1} \right)\left( {x-8} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 3} \right)\left( {x + 1} \right)\left( {\left( {x-7} \right)-\left( {x-8} \right)} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 3} \right)\left( {x + 1} \right)\left( {x-7-x + 8} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 3} \right)\left( {x + 1} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x + 3 = 0,}\\{x + 1 = 0\,}\end{array}} \right.\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = -3,}\\{x = -1.}\end{array}} \right.\)
Ответ: –3; –1.