$(x + 1) (x \cdot 2 - x + 1) - 2 x = x (x + 1) (x - 1)$

Answer

$x_{1} = 1.83929 x_{2} = - 0.41964 + 0.60629 i x_{3} = - 0.41964 - 0.60629 i$

Explanation

(x + 1) (x \cdot 2 - x + 1) - 2 x (x + 1) (x + 1) - 2 x x^{2} + x + x + 1 - 2 x x^{2} + 1 x^{2} + 1 x^{2} + 1 - x^{3} + x - x^{3} + x^{2} + x + 1 = x (x + 1) (x - 1) = (x^{2} + x) (x - 1) = x^{3} - x^{2} + x^{2} - x = x^{3} - x^{2} + x^{2} - x = x^{3} - x = 0 = 0 simplify left and right hand side move all terms to the left hand side simplify left side

This polynomial has no rational roots that can be found using Rational Root Test.

Roots were found using qubic formulas.

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(x+1)(x⋅2−x+1)−2x=x(x+1)(x−1)

x1​=1.83929​x2​=−0.41964+0.60629i​x3​=−0.41964−0.60629i​

$(x + 1) (x \cdot 2 - x + 1) - 2 x = x (x + 1) (x - 1)$

$x_{1} = 1.83929 x_{2} = - 0.41964 + 0.60629 i x_{3} = - 0.41964 - 0.60629 i$