1. **State the problem:** Solve the equation $$\frac{6}{x+3} = \frac{-2x}{x+3}$$ for $x$. 2. **Identify the domain restriction:** Since the denominators are $x+3$, we must have $x \neq -3$ to avoid division by zero. 3. **Multiply both sides by $x+3$ to eliminate the denominators:** $$\cancel{\frac{6}{x+3}} \times (x+3) = \cancel{\frac{-2x}{x+3}} \times (x+3)$$ which simplifies to $$6 = -2x$$ 4. **Solve for $x$:** $$6 = -2x$$ Divide both sides by $-2$: $$\frac{6}{\cancel{-2}} = \frac{-2x}{\cancel{-2}} \Rightarrow -3 = x$$ 5. **Check the solution against the domain restriction:** $x = -3$ is not allowed because it makes the denominator zero. 6. **Conclusion:** There is no solution to the equation because the only candidate $x = -3$ is excluded from the domain. **Final answer:** No solution.