Verified answer

[tex]\displaystyle\bf\\\underbrace{(x-1)(x^{2} +x+1)}_{x^{3} -1^{3} }+x^{2} =x^{2} (x+1)-2x\\\\\\x^{3} -1+x^{2} =x^{3} +x^{2} -2x\\\\\\x^{3} +x^{2} -x^{3} -x^{2} +2x=1\\\\\\2x=1\\\\\\\boxed{x=0,5}[/tex]