Let's solve the equation step by step:
1. **Original equation:**
$$4 - 7.5(x + 9) = -74.3$$
2. **Distribute -7.5:**
$$4 - 7.5x - 67.5 = -74.3$$
3. **Combine constants on the left side:**
$$-7.5x - 63.5 = -74.3$$
4. **Add 63.5 to both sides:**
$$-7.5x = -74.3 + 63.5$$
$$-7.5x = -10.8$$
5. **Divide both sides by -7.5:**
$$x = \frac{-10.8}{-7.5}$$
$$x = 1.44$$
Therefore, the solution to the equation is (x = 1.44).
**Final Answer:** The final answer is $$\boxed{1.44}$$