$$ \begin{aligned} -7+4m+10 &= 15-2m&& \text{simplify left and right hand side} \\[1 em]4m+3 &= -2m+15&& \text{move the $ \color{blue}{ -2m } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]4m+2m &= 15-3&& \text{simplify left and right hand side} \\[1 em]6m &= 12&& \text{ divide both sides by $ 6 $ } \\[1 em]m &= \frac{12}{6}&& \\[1 em]m &= 2&& \\[1 em] \end{aligned} $$

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