It looks like you've provided a quadratic expression: \( x^2 + 4x - 21 \).

Would you like to solve for \( x \) by factoring, or would you prefer using the quadratic formula? Let me know which method you'd like, or if you'd like both approaches explained!

For now, I’ll factor the expression:

1. We need two numbers that multiply to give \(-21\) and add up to \(4\). Those numbers are \(7\) and \(-3\).
   
2. So, the factored form of \( x^2 + 4x - 21 \) is:
   \[
   (x + 7)(x - 3)
   \]

To solve for \( x \):
   \[
   x + 7 = 0 \quad \text{or} \quad x - 3 = 0
   \]
   \[
   x = -7 \quad \text{or} \quad x = 3
   \]

Thus, the solutions are \( x = -7 \) and \( x = 3 \).

Do you need further clarification on any steps, or would you like additional methods?

### Related Questions:
1. How do you factor more complex quadratic expressions?
2. What is the quadratic formula and how is it derived?
3. How do you complete the square for quadratic equations?
4. Can quadratic equations have complex solutions?
5. How are quadratic equations applied in real-world problems?

**Tip**: Always check your factored solutions by multiplying the factors back to verify the original expression.

Discover how to solve the quadratic equation x^2 + 4x − 21 by factoring. This step-by-step guide is ideal for students in Grades 8-10 and covers key algebraic concepts, including factorization and the quadratic equation formula.

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