1. **Problem:** Solve the quadratic equation $x^2 + 4x + 3 = 0$ by factoring. 2. **Formula and rules:** To solve by factoring, first set the equation equal to zero, then factor the quadratic expression into two binomials. Use the zero product property: if $ab=0$, then $a=0$ or $b=0$. 3. **Step 1:** The equation is already set to zero: $x^2 + 4x + 3 = 0$. 4. **Step 2:** Factor the quadratic. Find two numbers that multiply to $3$ and add to $4$. These are $1$ and $3$. $$x^2 + 4x + 3 = (x + 1)(x + 3)$$ 5. **Step 3:** Set each factor equal to zero: $$x + 1 = 0 \quad \Rightarrow \quad x = -1$$ $$x + 3 = 0 \quad \Rightarrow \quad x = -3$$ 6. **Step 4:** Write the solution set: $$\boxed{\{-3, -1\}}$$ This means the roots or zeros of the quadratic are $x = -3$ and $x = -1$. **Summary:** We factored the quadratic into $(x+1)(x+3)$ and used the zero product property to find the solutions.