Verified answer

[tex]\displaystyle\bf\\(x^{3} +1)(x-3)+(2x-1)(x^{2} -x+1)=0\\\\(x +1)(x^{2} -x+1)(x-3)+(2x-1)(x^{2} -x+1)=0\\\\(x^{2} -x+1)\Big[(x+1)(x-3)+2x-1\Big]=0\\\\(x^{2} -x+1)(x^{2} -3x+x-3+2x-1)=0\\\\(x^{2} -x+1)(x^{2} -4)=0\\\\(x^{2} -x+1)(x-2)(x+2)=0\\\\\\\left[\begin{array}{ccc}x^{2} -x+1=0\\x-2=0\\x+2=0\end{array}\right\\\\\\\left[\begin{array}{ccc}D < 0 \ , \ x\oslash\\x_{1}=2 \\x_{2}=-2 \end{array}\right\\\\\\Otvet \ : \ 2 \ ; \ -2[/tex]