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