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 7x7 + 2x - 14 = 0 x2 - 10x + 25 = 0 6x2 + 5 = 0 x2 + 5x - 14 = 0 8x -2x +1 = 0 3x2 + 12x = 0 x2 - 3x - 4 = 0 10х2 + 1 - 20 = 0 x* +8 = 0 2x2 - 8x + 6 = 0 4x2 + 9x + 2 = 0 5x2 - 5x = 0 x2+ x - 6=0 3x- - 27 = 0 2x2 + 3x + 1 = 0 x2 - 8x + 16 = 0 x2 + 10x + 25 = 0 6x2 - 12x = 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!