1. **State the problem:** Solve the equation $$-3(2x + 1) = 5(5 - 4x)$$ for $x$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$-3 \times 2x = -6x$$ $$-3 \times 1 = -3$$ $$5 \times 5 = 25$$ $$5 \times (-4x) = -20x$$ So the equation becomes: $$-6x - 3 = 25 - 20x$$ 3. **Collect like terms:** Add $20x$ to both sides to get all $x$ terms on one side. $$-6x - 3 + 20x = 25 - 20x + 20x$$ $$(-6x + 20x) - 3 = 25$$ $$14x - 3 = 25$$ 4. **Isolate the variable term:** Add $3$ to both sides. $$14x - 3 + 3 = 25 + 3$$ $$14x = 28$$ 5. **Solve for $x$ by dividing both sides by 14:** $$x = \frac{28}{14}$$ Show cancelation: $$x = \frac{\cancel{28}}{\cancel{14}} = 2$$ 6. **Final answer:** $$\boxed{2}$$ The solution is $x = 2$.