x2-4x+3 =0 2x2 + 5x - 3 = 0 3x2 - 12 = 0 x2 + 6x + 9 = 0 x2 -2x - 8=0 4x2 + x - 10 = 0 5x2 - 20x + 15 = 0 x* + 4x = 0 9x2 - 24x + 16 = 0 2x2 - 3x + 1 = 0 x₴ - 6 = 0 x2 + 2x+1=0…

Let's solve each of the quadratic equations step by step.

1. Equation: \( x^2 - 4x + 3 = 0 \)

   • Factor: \( (x - 1)(x - 3) = 0 \)
   • Solutions: \( x = 1, 3 \)

2. Equation: \( 2x^2 + 5x - 3 = 0 \)

   • Using the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-5 \pm \sqrt{25 + 24}}{4} = \frac{-5 \pm 7}{4} \]
   • Solutions: \( x = \frac{1}{2}, -3 \)

3. Equation: \( 3x^2 - 12 = 0 \)

   • Rearranging gives: \( 3x^2 = 12 \) or \( x^2 = 4 \)
   • Solutions: \( x = 2, -2 \)

4. Equation: \( x^2 + 6x + 9 = 0 \)

   • Factor: \( (x + 3)^2 = 0 \)
   • Solution: \( x = -3 \) (double root)

5. Equation: \( x^2 - 2x - 8 = 0 \)

   • Factor: \( (x - 4)(x + 2) = 0 \)
   • Solutions: \( x = 4, -2 \)

6. Equation: \( 4x^2 + x - 10 = 0 \)

   • Using the quadratic formula: \[ x = \frac{-1 \pm \sqrt{1 + 160}}{8} = \frac{-1 \pm 13}{8} \]
   • Solutions: \( x = \frac{3}{4}, -\frac{7}{4} \)

7. Equation: \( 5x^2 - 20x + 15 = 0 \)

   • Divide by 5: \( x^2 - 4x + 3 = 0 \)
   • Solutions: \( x = 1, 3 \)

8. Equation: \( x^2 + 4x = 0 \)

   • Factor: \( x(x + 4) = 0 \)
   • Solutions: \( x = 0, -4 \)

9. Equation: \( 9x^2 - 24x + 16 = 0 \)

   • Using the quadratic formula: \[ x = \frac{24 \pm \sqrt{576 - 576}}{18} = \frac{24}{18} = \frac{4}{3} \]
   • Solution: \( x = \frac{4}{3} \) (double root)

10. Equation: \( 2x^2 - 3x + 1 = 0 \)

• Using the quadratic formula: \[ x = \frac{3 \pm \sqrt{(-3)^2 - 4 \cdot 2 \cdot 1}}{2 \cdot 2} = \frac{3 \pm 1}{4} \]
• Solutions: \( x = 1, \frac{1}{2} \)

11. Equation: \( x^2 - 6 = 0 \)

• Rearranging gives: \( x^2 = 6 \)
• Solutions: \( x = \sqrt{6}, -\sqrt{6} \)

12. Equation: \( x^2 + 2x + 1 = 0 \)

• Factor: \( (x + 1)^2 = 0 \)
• Solution: \( x = -1 \) (double root)

13. Equation: \( 7x^2 + 2x - 14 = 0 \)

• Using the quadratic formula: \[ x = \frac{-2 \pm \sqrt{4 + 392}}{14} \]
• Solutions: \( x = \frac{-1 \pm \sqrt{99}}{7} \)

14. Equation: \( x^2 - 10x + 25 = 0 \)

• Factor: \( (x - 5)^2 = 0 \)
• Solution: \( x = 5 \) (double root)

15. Equation: \( 6x^2 + 5 = 0 \)

• Rearranging gives: \( 6x^2 = -5 \)
• Solutions: \( x = \pm \frac{\sqrt{30}}{6} \) (complex solutions)

16. Equation: \( x^2 + 5x - 14 = 0 \)

• Using the quadratic formula: \[ x = \frac{-5 \pm \sqrt{25 + 56}}{2} = \frac{-5 \pm 9}{2} \]
• Solutions: \( x = 2, -7 \)

17. Equation: \( 8x - 2x + 1 = 0 \)

• Simplifies to \( 6x + 1 = 0 \)
• Solution: \( x = -\frac{1}{6} \)

18. Equation: \( 3x^2 + 12x = 0 \)

• Factor: \( 3x(x + 4) = 0 \)
• Solutions: \( x = 0, -4 \)

19. Equation: \( x^2 - 3x - 4 = 0 \)

• Factor: \( (x - 4)(x + 1) = 0 \)
• Solutions: \( x = 4, -1 \)

20. Equation: \( 10x^2 + 1 - 20 = 0 \)

• Rearranging gives: \( 10x^2 = 19 \)
• Solutions: \( x = \pm \sqrt{\frac{19}{10}} = \pm \frac{\sqrt{190}}{10} \)

21. Equation: \( x^2 + 8 = 0 \)

• Rearranging gives: \( x^2 = -8 \)
• Solutions: \( x = \pm 2i\sqrt{2} \)

22. Equation: \( 2x^2 - 8x + 6 = 0 \)

• Using the quadratic formula: \[ x = \frac{8 \pm \sqrt{64 - 48}}{4} = \frac{8 \pm 4}{4} \]
• Solutions: \( x = 3, 1 \)

23. Equation: \( 4x^2 + 9x + 2 = 0 \)

• Using the quadratic formula: \[ x = \frac{-9 \pm \sqrt{81 - 32}}{8} = \frac{-9 \pm \sqrt{49}}{8} \]
• Solutions: \( x = -1, -\frac{1}{4} \)

24. Equation: \( 5x^2 - 5x = 0 \)

• Factor: \( 5x(x - 1) = 0 \)
• Solutions: \( x = 0, 1 \)

25. Equation: \( x^2 + x - 6 = 0 \)

• Factor: \( (x - 2)(x + 3) = 0 \)
• Solutions: \( x = 2, -3 \)

26. Equation: \( 3x - 27 = 0 \)

• Rearranging gives: \( 3x = 27 \)
• Solution: \( x = 9 \)

27. Equation: \( 2x^2 + 3x + 1 = 0 \)

• Using the quadratic formula: \[ x = \frac{-3 \pm \sqrt{9 - 8}}{4} = \frac{-3 \pm 1}{4} \]
• Solutions: \( x = -\frac{1}{2}, -1 \)

28. Equation: \( x^2 - 8x + 16 = 0 \)

• Factor: \( (x - 4)^2 = 0 \)
• Solution: \( x = 4 \) (double root)

29. Equation: \( x^2 + 10x + 25 = 0 \)

• Factor: \( (x + 5)^2 = 0 \)
• Solution: \( x = -5 \) (double root)

30. Equation: \( 6x^2 - 12x = 0 \)

• Factor: \( 6x(x - 2) = 0 \)
• Solutions: \( x = 0, 2 \)

These are the steps and solutions for each of the listed equations. If you have any specific question or need further clarification, feel free to ask!