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Let's solve the quadratic equation provided by factoring. The equation is:

\[
x^2 + 3x - 43 = -3x - 3
\]

### Step 1: Bring all terms to one side of the equation
Move all terms from the right-hand side to the left-hand side by adding \(3x + 3\) to both sides:

\[
x^2 + 3x - 43 + 3x + 3 = 0
\]

Simplify:

\[
x^2 + 6x - 40 = 0
\]

### Step 2: Factor the quadratic equation
Now we will factor the quadratic expression \(x^2 + 6x - 40\).

We are looking for two numbers that multiply to \(-40\) and add to \(6\). These numbers are \(10\) and \(-4\) because:

\[
10 \times (-4) = -40 \quad \text{and} \quad 10 + (-4) = 6
\]

So, the factorization is:

\[
(x + 10)(x - 4) = 0
\]

### Step 3: Solve for \(x\)
Set each factor equal to zero:

\[
x + 10 = 0 \quad \text{or} \quad x - 4 = 0
\]

Solving these gives:

\[
x = -10 \quad \text{or} \quad x = 4
\]

### Final Answer:
The solutions are \(x = -10\) and \(x = 4\).

Would you like more details or have any questions?

Here are some related questions for practice:
1. How do you verify the solutions by substituting back into the original equation?
2. What is the graphical interpretation of the solutions for a quadratic equation?
3. What other methods, besides factoring, can be used to solve this quadratic equation?
4. Can all quadratic equations be factored? Why or why not?
5. What happens if the quadratic equation has no real solutions?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy it!

Solve the quadratic by factoring: x^2 + 3x - 43 = -3x - 3.

Learn how to solve the quadratic equation x^2 + 6x - 40 by factoring. This step-by-step guide breaks down the problem-solving process, including factoring and using the zero-product property. Suitable for students in Grades 7-9.

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