1. **State the problem:** Solve the equation $7(x-3)=2(x+7)$ for $x$. 2. **Write the formula and rules:** Use the distributive property to expand both sides: $a(b+c) = ab + ac$. 3. **Expand both sides:** $$7(x-3) = 7x - 21$$ $$2(x+7) = 2x + 14$$ So the equation becomes: $$7x - 21 = 2x + 14$$ 4. **Isolate variable terms on one side:** Subtract $2x$ from both sides: $$7x - 21 - 2x = 2x + 14 - 2x$$ $$5x - 21 = 14$$ 5. **Isolate constant terms on the other side:** Add $21$ to both sides: $$5x - 21 + 21 = 14 + 21$$ $$5x = 35$$ 6. **Solve for $x$ by dividing both sides by 5:** $$x = \frac{35}{5}$$ Show cancellation: $$x = \frac{\cancel{35}}{\cancel{5}} = 7$$ 7. **Final answer:** $$\boxed{7}$$