1. **State the problem:** Solve the equation $$3(1 + 11x) = -5(-3 - x) - 12$$ for $x$. 2. **Apply the distributive property:** Multiply out the parentheses on both sides. $$3 \times 1 + 3 \times 11x = -5 \times (-3) - 5 \times (-x) - 12$$ which simplifies to $$3 + 33x = 15 + 5x - 12$$ 3. **Simplify the right side:** Combine like terms. $$3 + 33x = (15 - 12) + 5x$$ $$3 + 33x = 3 + 5x$$ 4. **Isolate the variable terms:** Subtract 3 from both sides. $$\cancel{3} + 33x - \cancel{3} = \cancel{3} + 5x - \cancel{3}$$ $$33x = 5x$$ 5. **Subtract $5x$ from both sides to get all $x$ terms on one side:** $$33x - 5x = 5x - 5x$$ $$28x = 0$$ 6. **Divide both sides by 28 to solve for $x$:** $$\frac{28x}{\cancel{28}} = \frac{0}{\cancel{28}}$$ $$x = 0$$ **Final answer:** $$x = 0$$