To solve the equation \( x^2 + 4x = -3 \), let's go through the following steps:

### Step 1: Move all terms to one side of the equation.
We want the equation in standard quadratic form, \( ax^2 + bx + c = 0 \). So, add 3 to both sides:

\[
x^2 + 4x + 3 = 0
\]

### Step 2: Factor the quadratic equation.
Now, we look for two numbers that multiply to give \( 3 \) and add up to \( 4 \). The numbers are \( 1 \) and \( 3 \):

\[
x^2 + 4x + 3 = (x + 1)(x + 3) = 0
\]

### Step 3: Solve for \( x \).
Using the zero-product property, set each factor equal to zero:

\[
x + 1 = 0 \quad \text{or} \quad x + 3 = 0
\]

Solving each equation gives:

\[
x = -1 \quad \text{or} \quad x = -3
\]

### Final Answer:
The solutions are \( x = -1 \) and \( x = -3 \).

Would you like more details or have any questions?

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Here are five related questions to consider:
1. What if the constant on the right side of the equation was different, such as \( -5 \)?
2. How would you solve the equation using the quadratic formula instead of factoring?
3. Can all quadratic equations be factored easily, and if not, why?
4. What are some real-world applications of quadratic equations?
5. How does completing the square work to solve quadratic equations?

**Tip:** Always check your solutions by plugging them back into the original equation to verify that they satisfy the equation!

Learn how to solve the quadratic equation x^2 + 4x + 3 = 0 by factoring. This step-by-step guide covers algebraic concepts, including the zero-product property and factoring methods. Suitable for Grades 7-9 students, this lesson explains how to find the roots of the equation.

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