1. **State the problem:** Solve the quadratic equation $x^2 + 5x = 0$. 2. **Formula and rules:** To solve quadratic equations, one common method is factoring. If the equation can be factored into a product of terms equal to zero, then by the zero product property, at least one of the factors must be zero. 3. **Factor the equation:** $$x^2 + 5x = x(x + 5) = 0$$ 4. **Apply zero product property:** Set each factor equal to zero: $$x = 0$$ $$x + 5 = 0$$ 5. **Solve each equation:** $$x = 0$$ $$x = -5$$ 6. **Final answer:** The solutions to the equation are $x = 0$ and $x = -5$. These are the values of $x$ that satisfy the original equation.