Solve x² + 5x + 6 = 0

Step-by-step solution

1. Look for two numbers that multiply to $6$ (the constant term) and add to $5$ (the linear coefficient).

2. The pair $2$ and $3$ satisfies both: $2 \times 3 = 6$ and $2 + 3 = 5$.

3. Factor the quadratic: $x^2 + 5x + 6 = (x + 2)(x + 3)$.

4. Set each factor to zero: $x + 2 = 0$ or $x + 3 = 0$.

5. Solve each: $x = -2$ or $x = -3$.