$$ \begin{aligned} (x-1)^2 &= (x+1)^2&& \text{simplify left and right hand side} \\[1 em]x^2-2x+1 &= x^2+2x+1&& \text{move all terms to the left hand side } \\[1 em]x^2-2x+1-x^2-2x-1 &= 0&& \text{simplify left side} \\[1 em]x^2-2x+1-x^2-2x-1 &= 0&& \\[1 em]-4x &= 0&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= \frac{0}{-4}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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