1. **State the problem:** Solve the equation $3(x + 5) + 2(2x + 3) = 0$ for $x$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$3(x + 5) = 3x + 15$$ $$2(2x + 3) = 4x + 6$$ So the equation becomes: $$3x + 15 + 4x + 6 = 0$$ 3. **Combine like terms:** $$3x + 4x + 15 + 6 = 0$$ $$7x + 21 = 0$$ 4. **Isolate the variable term:** Subtract 21 from both sides. $$7x + 21 - 21 = 0 - 21$$ $$7x = -21$$ 5. **Solve for $x$ by dividing both sides by 7:** $$\frac{\cancel{7}x}{\cancel{7}} = \frac{-21}{7}$$ $$x = -3$$ **Final answer:** $x = -3$