$$ \begin{aligned} 6-4x &= 7x-9x+6&& \text{simplify left and right hand side} \\[1 em]-4x+6 &= -2x+6&& \text{move the $ \color{blue}{ -2x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]-4x+2x &= 6-6&& \text{simplify left and right hand side} \\[1 em]-2x &= 0&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{0}{-2}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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