$$ \begin{aligned} 3 \cdot \frac{2-c}{2} &= -2 \cdot \frac{2c+3}{5}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot3 \cdot \frac{2-c}{2} &= -10\cdot2 \cdot \frac{2c+3}{5}&& \text{cancel out the denominators} \\[1 em]-15c+30 &= -(8c+12)&& \text{simplify right side} \\[1 em]-15c+30 &= -8c-12&& \text{move the $ \color{blue}{ -8c } $ to the left side and $ \color{blue}{ 30 }$ to the right} \\[1 em]-15c+8c &= -12-30&& \text{simplify left and right hand side} \\[1 em]-7c &= -42&& \text{ divide both sides by $ -7 $ } \\[1 em]c &= \frac{-42}{-7}&& \\[1 em]c &= 6&& \\[1 em] \end{aligned} $$

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