The expression you've provided is a quadratic equation: \( x^2 + 5x + 6 \). To solve this equation, we can factor it.

### Step 1: Factor the quadratic expression
We need to find two numbers that multiply to the constant term (6) and add to the coefficient of the linear term (5).

The two numbers are 2 and 3 because:
\[ 2 \times 3 = 6 \]
\[ 2 + 3 = 5 \]

So, we can factor the quadratic as:
\[ x^2 + 5x + 6 = (x + 2)(x + 3) \]

### Step 2: Solve the equation
To find the roots (solutions), set each factor equal to zero:
\[
x + 2 = 0 \quad \text{or} \quad x + 3 = 0
\]
Solve for \( x \) in each case:
\[
x = -2 \quad \text{or} \quad x = -3
\]

### Final Answer:
The solutions to the equation \( x^2 + 5x + 6 = 0 \) are \( x = -2 \) and \( x = -3 \).

Would you like more details or have any questions? 

Here are some related questions you might find interesting:

1. What are the roots of the equation \( x^2 - 7x + 10 \)?
2. How can we factor a quadratic equation when it has no real roots?
3. What is the quadratic formula and how is it used?
4. How do you complete the square for the equation \( x^2 + 6x + 8 \)?
5. What is the difference between factoring and using the quadratic formula to solve equations?

**Tip:** When factoring quadratics, always check if the equation can be factored easily before using more complex methods like the quadratic formula.

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 finding roots. Suitable for students in Grades 7-9.

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