$$ \begin{aligned} \frac{x\cdot4-8x\cdot3+2x-28}{x-4} &= 0&& \text{multiply ALL terms by } \color{blue}{ x-4 }. \\[1 em](x-4)\frac{x\cdot4-8x\cdot3+2x-28}{x-4} &= (x-4)\cdot0&& \text{cancel out the denominators} \\[1 em]-18x-28 &= 0&& \text{ move the constants to the right } \\[1 em]-18x &= 28&& \text{ divide both sides by $ -18 $ } \\[1 em]x &= -\frac{28}{18}&& \\[1 em]x &= -\frac{14}{9}&& \\[1 em] \end{aligned} $$

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