Question: 2+3\cdot(-2-28x)+ x5=2-x-4+23 \cdot(x+3)
1. **State the problem:** Simplify and solve the equation $$2+3\cdot(-2-28x)+ x5=2-x-4+23 \cdot(x+3)$$ for $x$.
2. **Rewrite the equation clearly:**
$$2 + 3(-2 - 28x) + 5x = 2 - x - 4 + 23(x + 3)$$
3. **Apply the distributive property:**
$$2 + 3 \times (-2) + 3 \times (-28x) + 5x = 2 - x - 4 + 23x + 69$$
4. **Calculate the multiplications:**
$$2 - 6 - 84x + 5x = 2 - x - 4 + 23x + 69$$
5. **Combine like terms on each side:**
Left side: $$2 - 6 = -4$$ so $$-4 - 84x + 5x = -4 - 79x$$
Right side: $$2 - 4 + 69 = 67$$ so $$67 - x + 23x = 67 + 22x$$
6. **Rewrite the simplified equation:**
$$-4 - 79x = 67 + 22x$$
7. **Add $79x$ to both sides to gather $x$ terms on the right:**
$$-4 = 67 + 22x + 79x$$
$$-4 = 67 + 101x$$
8. **Subtract 67 from both sides:**
$$-4 - 67 = 101x$$
$$-71 = 101x$$
9. **Divide both sides by 101 to solve for $x$:**
$$x = \frac{-71}{101}$$
10. **Final answer:**
$$x = -\frac{71}{101}$$