\(\left(x-3\right)\left(9+x^2+3x\right)+\left(2+x\right).x\left(-x+2\right)=1\)
\(\Leftrightarrow\left(x-3\right)\left(x^2+3x+3^2\right)+x\left(2+x\right)\left(2-x\right)-1=0\)\(\Leftrightarrow x^3-27+x\left(4-x^2\right)-1=0\)
\(\Leftrightarrow x^3-27+4x-x^3=0\)
\(\Leftrightarrow4x=27\Rightarrow x=\dfrac{27}{4}\)