Решите уравнение: x(x-2)(x-3)=8+x(x-2,5)^2.

\[x(x - 2)(x - 3) =\]

\[= 8 + x(x - 2,5)²\]

\[x\left( x^{2} - 5x + 6 \right) =\]

\[= 8 + x\left( x^{2} - 5x + 6,25 \right)\]

\[x^{3} - 5x^{2} + 6x =\]

\[= 8 + x^{3} - 5x^{2} - 6,25x\]

\[0,25x = - 8\]

\[x = - 32\]

\[Ответ:\ x = - 32.\]