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

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