Certainly! Here are 30 problems similar to the equation \( z^2 - 12 = 4z \), which involve solving quadratic equations by factoring:

1. \( x^2 - 5x = 14 \)
2. \( y^2 + 10y = 25 \)
3. \( a^2 - 9 = 6a \)
4. \( b^2 + 7b = 10 \)
5. \( c^2 - 4c = 20 \)
6. \( d^2 + 12 = 8d \)
7. \( e^2 - 3e = 18 \)
8. \( f^2 + 8 = 6f \)
9. \( g^2 - 7g = 10 \)
10. \( h^2 + 15 = 5h \)
11. \( i^2 - 2i = 24 \)
12. \( j^2 + 11j = 30 \)
13. \( k^2 - 6 = 9k \)
14. \( m^2 + 4m = 16 \)
15. \( n^2 - 10n = 25 \)
16. \( p^2 + 3p = 21 \)
17. \( q^2 - 8 = 7q \)
18. \( r^2 + 14r = 49 \)
19. \( s^2 - 13 = 5s \)
20. \( t^2 + 6t = 9 \)
21. \( u^2 - 11u = 30 \)
22. \( v^2 + 9 = 6v \)
23. \( w^2 - 4w = 28 \)
24. \( x^2 + 13x = 36 \)
25. \( y^2 - 2y = 35 \)
26. \( z^2 + 5 = 3z \)
27. \( a^2 - 6a = 8 \)
28. \( b^2 + 7 = 2b \)
29. \( c^2 - 9c = 40 \)
30. \( d^2 + 10d = 24 \)

These problems all involve quadratic equations that can be solved by moving all terms to one side of the equation, factoring, and then solving for the variable.

Would you like detailed solutions for any of these problems, or do you have any other questions?

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Here are 5 relative questions:

1. How do you determine the correct factors of a quadratic equation?
2. What are the possible scenarios when solving quadratic equations by factoring?
3. How do you handle quadratic equations that cannot be factored easily?
4. What is the quadratic formula, and when should it be used?
5. How do you graph the solutions to a quadratic equation?

**Tip:** Always check for possible common factors before factoring the quadratic equation. This can simplify the process and help avoid mistakes.

Explore how to solve the quadratic equation z^2 - 12 = 4z step-by-step with detailed solutions. This problem involves factoring quadratic equations and applying the quadratic formula. Suitable for high school students.

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