$$ \begin{aligned} x\cdot2-2 \cdot \frac{x}{x-2}(x+3) &= 0&& \text{multiply ALL terms by } \color{blue}{ x-2 }. \\[1 em](x-2)x\cdot2-(x-2)2 \cdot \frac{x}{x-2}(x+3) &= (x-2)\cdot0&& \text{cancel out the denominators} \\[1 em]2x^2-4x-(2x^2+6x) &= 0&& \text{simplify left side} \\[1 em]2x^2-4x-2x^2-6x &= 0&& \\[1 em]2x^2-4x-2x^2-6x &= 0&& \\[1 em]-10x &= 0&& \text{ divide both sides by $ -10 $ } \\[1 em]x &= \frac{0}{-10}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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