The given expression is a quadratic equation:

\[
x^2 + 5x + 6 = 0
\]

We can factor the quadratic expression to solve for \(x\). First, we look for two numbers that multiply to give 6 (the constant term) and add up to 5 (the coefficient of \(x\)).

The numbers 2 and 3 work, because:

\[
2 \times 3 = 6 \quad \text{and} \quad 2 + 3 = 5
\]

So, we can factor the quadratic as:

\[
(x + 2)(x + 3) = 0
\]

Setting each factor equal to zero:

\[
x + 2 = 0 \quad \text{or} \quad x + 3 = 0
\]

Solving these:

\[
x = -2 \quad \text{or} \quad x = -3
\]

Thus, the solutions are \(x = -2\) and \(x = -3\).

Would you like further details on any of the steps?

### Related Questions:
1. How can you verify the solution to a factored quadratic?
2. What are other methods to solve quadratic equations besides factoring?
3. Can every quadratic equation be factored?
4. How does the discriminant help in solving quadratic equations?
5. What is the significance of the solutions to quadratic equations in real-world problems?

**Tip:** When factoring quadratics, always check if the equation can be simplified before factoring to avoid unnecessary complexity.

Learn how to solve the quadratic equation x^2 + 5x + 6 using the factoring method. This step-by-step guide covers essential algebraic techniques suitable for Grades 7-9 students, including factoring and solving quadratic equations.

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