$$ \begin{aligned} 10-x+2 &= x&& \text{simplify left side} \\[1 em]-x+12 &= x&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]-x-x &= -12&& \text{simplify left side} \\[1 em]-2x &= -12&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-12}{-2}&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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