1. **State the problem:** Solve the equation $-7 + 4m + 10 = 15 - 2m$ for $m$. 2. **Combine like terms on the left side:** $-7 + 10 = 3$, so the equation becomes $3 + 4m = 15 - 2m$. 3. **Add $2m$ to both sides to get all $m$ terms on one side:** $3 + 4m + 2m = 15$, which simplifies to $3 + 6m = 15$. 4. **Subtract 3 from both sides to isolate the $m$ term:** $6m = 15 - 3$, so $6m = 12$. 5. **Divide both sides by 6 to solve for $m$:** $m = \frac{12}{6} = 2$. **Final answer:** $m = 2$.