1. **State the problem:** Solve the equation $3(5x-29)-9=-6$ for $x$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses: $$3 \times 5x = 15x$$ $$3 \times (-29) = -87$$ So the equation becomes: $$15x - 87 - 9 = -6$$ 3. **Combine like terms:** $$-87 - 9 = -96$$ So the equation simplifies to: $$15x - 96 = -6$$ 4. **Isolate the variable term:** Add 96 to both sides: $$15x = -6 + 96$$ $$15x = 90$$ 5. **Solve for $x$:** Divide both sides by 15: $$x = \frac{90}{15} = 6$$ **Final answer:** $$x = 6$$