1. **State the problem:** Solve the quadratic equation $$x^2 + 19x = 0$$ by factoring. 2. **Write the equation:** $$x^2 + 19x = 0$$ 3. **Factor the equation:** Factor out the common factor $x$: $$x(x + 19) = 0$$ 4. **Apply the zero product property:** For the product to be zero, either factor must be zero: $$x = 0 \quad \text{or} \quad x + 19 = 0$$ 5. **Solve each equation:** - For $x = 0$, the solution is $0$. - For $x + 19 = 0$, subtract $19$ from both sides: $$x + 19 = 0$$ $$x = \cancel{+19} - 19$$ $$x = -19$$ 6. **Final solution set:** $$\boxed{0, -19}$$ These are the values of $x$ that satisfy the original equation.