1. **State the problem:** Solve the equation $$\frac{xe^x - 3e^x}{5x^2 - 20x + 20} = 0$$ for $x$. 2. **Understand the zero fraction rule:** A fraction equals zero if and only if its numerator is zero and the denominator is not zero. 3. **Set the numerator equal to zero:** $$xe^x - 3e^x = 0$$ 4. **Factor out the common term $e^x$:** $$e^x(x - 3) = 0$$ 5. Since $e^x \neq 0$ for all real $x$, the equation reduces to: $$x - 3 = 0$$ 6. **Solve for $x$:** $$x = 3$$ 7. **Check the denominator at $x=3$ to ensure it is not zero:** $$5(3)^2 - 20(3) + 20 = 5 \times 9 - 60 + 20 = 45 - 60 + 20 = 5 \neq 0$$ 8. Since the denominator is not zero at $x=3$, the solution is valid. **Final answer:** $$x = 3$$