$$ \begin{aligned} -x\cdot4+3x\cdot2-x+6-x\cdot4-x\cdot3+2x\cdot2-5 &= 0&& \text{simplify left side} \\[1 em]-x\cdot4+3x\cdot2-x+6-x\cdot4-x\cdot3+2x\cdot2-5 &= 0&& \\[1 em]-4x+6x-x+6-4x-3x+4x-5 &= 0&& \\[1 em]-4x+6x-x+6-4x-3x+4x-5 &= 0&& \\[1 em]-2x+1 &= 0&& \text{ move the constants to the right } \\[1 em]-2x &= -1&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-1}{-2}&& \\[1 em]x &= \frac{1}{2}&& \\[1 em] \end{aligned} $$

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