$$ \begin{aligned} x\cdot2+4x-\frac{1}{2}(x+4)\frac{x}{4} &= x\cdot2+4x-8&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4x\cdot2+4\cdot4x-4 \cdot \frac{1}{2}(x+4)\frac{x}{4} &= 4x\cdot2+4\cdot4x-4\cdot8&& \text{cancel out the denominators} \\[1 em]8x+16x-\frac{1}{2}(x+4)x &= 8x+16x-32&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot8x+2\cdot16x-2 \cdot \frac{1}{2}(x+4)x &= 2\cdot8x+2\cdot16x-2\cdot32&& \text{cancel out the denominators} \\[1 em]16x+32x-(x^2+4x) &= 16x+32x-64&& \text{simplify left and right hand side} \\[1 em]48x-(x^2+4x) &= 48x-64&& \\[1 em]48x-x^2-4x &= 48x-64&& \\[1 em]-x^2+44x &= 48x-64&& \text{move all terms to the left hand side } \\[1 em]-x^2+44x-48x+64 &= 0&& \text{simplify left side} \\[1 em]-x^2-4x+64 &= 0&& \\[1 em] \end{aligned} $$

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