$$(x+1)(x\cdot2-x+1)-2x = x(x+1)(x-1)$$
Answer
$$ \begin{matrix}x_1 = 1.83929 & x_2 = -0.41964+0.60629i & x_3 = -0.41964-0.60629i \end{matrix} $$
Explanation
$$ \begin{aligned} (x+1)(x\cdot2-x+1)-2x &= x(x+1)(x-1)&& \text{simplify left and right hand side} \\[1 em](x+1)(x+1)-2x &= (x^2+x)(x-1)&& \\[1 em]x^2+x+x+1-2x &= x^3-x^2+x^2-x&& \\[1 em]x^2+1 &= x^3-x^2+x^2-x&& \\[1 em]x^2+1 &= x^3-x&& \text{move all terms to the left hand side } \\[1 em]x^2+1-x^3+x &= 0&& \text{simplify left side} \\[1 em]-x^3+x^2+x+1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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