To solve the quadratic equation \(x^2 + 5x + 6 = 0\), we can factorize it. Here are the steps:

1. **Write down the equation**: 
   \[ x^2 + 5x + 6 = 0 \]

2. **Look for two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of x)**:
   \[ 2 \times 3 = 6 \]
   \[ 2 + 3 = 5 \]

3. **Factorize the quadratic equation using these two numbers**:
   \[ x^2 + 5x + 6 = (x + 2)(x + 3) = 0 \]

4. **Set each factor equal to zero and solve for x**:
   \[ x + 2 = 0 \quad \text{or} \quad x + 3 = 0 \]
   \[ x = -2 \quad \text{or} \quad x = -3 \]

So, the solutions to the quadratic equation \(x^2 + 5x + 6 = 0\) are \(x = -2\) and \(x = -3\).

Would you like any more details or have any questions?

Here are some related questions that might help you understand the topic better:

1. What is the general form of a quadratic equation?
2. How do you determine if a quadratic equation can be factored?
3. What are the methods to solve a quadratic equation if it cannot be factored easily?
4. Can you explain the quadratic formula and how it is derived?
5. How do you complete the square for a quadratic equation?
6. What are the properties of the solutions to a quadratic equation?
7. How does the discriminant help determine the nature of the roots of a quadratic equation?
8. How can you graph a quadratic function and what do its roots represent?

**Tip:** When solving quadratic equations, always check if the equation can be factored first, as it is often the simplest method.

Learn how to solve the quadratic equation x^2 + 5x + 6 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring quadratic equations and applying the quadratic formula theorem. Suitable for students in Grades 7-9.

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