Question
$$(x^2+x+1)(2x-1)-(x^2-x+1)(2x+1) = 0$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = -1 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (x^2+x+1)(2x-1)-(x^2-x+1)(2x+1) &= 0&& \text{simplify left side} \\[1 em]2x^3-x^2+2x^2-x+2x-1-(2x^3+x^2-2x^2-x+2x+1) &= 0&& \\[1 em]2x^3+x^2+x-1-(2x^3-x^2+x+1) &= 0&& \\[1 em]2x^3+x^2+x-1-2x^3+x^2-x-1 &= 0&& \\[1 em]2x^3+x^2+x-1-2x^3+x^2-x-1 &= 0&& \\[1 em]2x^2-2 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-2 = 0 $ is a quadratic equation.
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