\(\left(x-3\right)^3-\left(2x+1\right)\left(4x^2+1^2\right)=\left(x+2\right)^3-\left(2x-3\right)^3-18x\left(2x-3\right)\)\(\Leftrightarrow x^3-9x^2+27x-27-\left(8x^3+2x+4x^2+1\right)=x^3+6x^2+12x+8-\left(8x^3-36x^2+54x-27\right)-36x^2+54x\)\(\Leftrightarrow x^3-9x^2+27x-27-8x^3-2x-4x^2-1-x^3-6x^2-12x-8+8x^3-36x^2+54x-27+36x^2-54x=0\)\(\Leftrightarrow-19x^2+13x-9=0\)
\(\Leftrightarrow-19\left(x^2-\dfrac{13}{19}+\dfrac{169}{1444}\right)-\dfrac{515}{76}=0\)
\(\Leftrightarrow-19\left(x-\dfrac{13}{38}\right)^2=\dfrac{515}{76}\Rightarrow\left[{}\begin{matrix}x-\dfrac{13}{38}=\sqrt{\dfrac{515}{76}}\\x-\dfrac{13}{38}=-\sqrt{\dfrac{515}{76}}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{515}{76}}+\dfrac{13}{38}\\x=-\sqrt{\dfrac{515}{76}}+\dfrac{13}{38}\end{matrix}\right.\)
