Question: User: 3d-21(2d-4)=-45(4d-4)
1. **State the problem:** Solve the equation $$3d - 21(2d - 4) = -45(4d - 4)$$ for $d$.
2. **Distribute the constants inside the parentheses:**
$$3d - 21 \times 2d + 21 \times 4 = -45 \times 4d + 45 \times 4$$
which simplifies to
$$3d - 42d + 84 = -180d + 180$$
3. **Combine like terms on the left side:**
$$3d - 42d = -39d$$
So the equation becomes
$$-39d + 84 = -180d + 180$$
4. **Add $180d$ to both sides to get all $d$ terms on one side:**
$$-39d + 180d + 84 = -180d + 180 + 180d$$
which simplifies to
$$141d + 84 = 180$$
5. **Subtract $84$ from both sides:**
$$141d + \cancel{84} - \cancel{84} = 180 - 84$$
$$141d = 96$$
6. **Divide both sides by $141$ to solve for $d$:**
$$d = \frac{96}{141}$$
7. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor $3$:**
$$d = \frac{\cancel{96}^ {32}}{\cancel{141}^{47}}$$
**Final answer:**
$$d = \frac{32}{47}$$