1. **State the problem:** Solve the equation $3(a+2)-2a=\frac{1}{7}(-7a+42)$. 2. **Write down the equation:** $$3(a+2)-2a=\frac{1}{7}(-7a+42)$$ 3. **Distribute terms:** $$3a + 6 - 2a = \frac{1}{7}(-7a) + \frac{1}{7}(42)$$ $$3a + 6 - 2a = -a + 6$$ 4. **Simplify left side:** $$a + 6 = -a + 6$$ 5. **Add $a$ to both sides:** $$a + a + 6 = -a + a + 6$$ $$2a + 6 = 6$$ 6. **Subtract 6 from both sides:** $$2a + \cancel{6} - \cancel{6} = 6 - 6$$ $$2a = 0$$ 7. **Divide both sides by 2:** $$\frac{2a}{\cancel{2}} = \frac{0}{\cancel{2}}$$ $$a = 0$$ **Final answer:** $$a = 0$$