$$ \begin{aligned} (1+x)\cdot3-(1-x)\cdot3 &= 6(x+1)\cdot2&& \text{simplify left and right hand side} \\[1 em]3+3x-(3-3x) &= (6x+6)\cdot2&& \\[1 em]3+3x-3+3x &= 12x+12&& \\[1 em]3+3x-3+3x &= 12x+12&& \\[1 em]6x &= 12x+12&& \text{move the $ \color{blue}{ 12x } $ to the left side} \\[1 em]6x-12x &= 12&& \text{simplify left side} \\[1 em]-6x &= 12&& \text{ divide both sides by $ -6 $ } \\[1 em]x &= -\frac{12}{6}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$
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