Question: User: 828x+1440=0
1. **State the problem:** Solve the linear equation $$828x + 1440 = 0$$ for $$x$$.
2. **Formula and rules:** To solve for $$x$$, isolate $$x$$ by moving constants to the other side and then dividing by the coefficient of $$x$$.
3. **Isolate $$x$$:**
$$828x = -1440$$
4. **Divide both sides by 828:**
$$x = \frac{-1440}{828}$$
5. **Simplify the fraction:**
Find the greatest common divisor (GCD) of 1440 and 828, which is 12.
6. **Divide numerator and denominator by 12:**
$$x = \frac{\cancel{12} \times -120}{\cancel{12} \times 69} = \frac{-120}{69}$$
7. **Simplify further if possible:**
GCD of 120 and 69 is 3.
8. **Divide numerator and denominator by 3:**
$$x = \frac{\cancel{3} \times -40}{\cancel{3} \times 23} = \frac{-40}{23}$$
9. **Final answer:**
$$x = -\frac{40}{23}$$