1. 4x(x - 5) - (x - 1)(4x - 3) = 5
⇔ 4x² - 20x - 4x² + 3x + 4x - 3 - 5 = 0
⇔ - 13x - 8 = 0
⇔ - 13x = 8
⇔ x = - 8/13
2. 4x(x - 5) - 7x(x - 4) + 3x² = 12
⇔ 4x² - 20x - 7x² + 28x + 3x² -12 = 0
⇔ 8x - 12 = 0
⇔ 8x = 12
⇔ x = 3/2
3. (3x - 4)(x - 2) = 3x(x - 9) - 3
⇔ 3x² - 6x - 4x + 8 - 3x² + 27x + 3 = 0
⇔ 17x + 11 = 0
⇔ x = -11/17
4. (x - 5)(x - 4) - (x + 1)(x - 2) = 7
⇔ x² - 4x - 5x + 20 - x² + 2x - x + 2 - 7 = 0
⇔ - 8x +15 = 0
⇔ x = 15/8
5. 5x(x - 3) = (x - 2)(5x - 1) - 5
⇔ 5x² - 15x - 5x² + x + 10x - 2 + 5 = 0
⇔ - 4x + 3 = 0
⇔ x = 3/4
6. (x - 5)(x - 1) = (x - 1)(x - 2)
⇔ x² - x - 5x + 5 - x² + 2x + x - 2 = 0
⇔ -3x + 3 = 0
⇔ x = 1
7. 6(x - 3)(x - 4) - 6x(x - 2) = 4
⇔ 6x² - 24x - 18x + 72 - 6x² + 12x - 4 = 0
⇔ -30x + 68 = 0
⇔ x = 34/15
8. - (x + 3)(x - 4) + (x - 1)(x + 1) = 10
⇔ - x² + 4x - 3x + 12 + x² + x - x - 1 - 10 = 0
⇔ x + 1 = 0
⇔ x = - 1
9. (2x - 1)(x - 2) - (x + 3)(2x - 7) = 3
⇔ 2x² - 4x - x + 2 - 2x² + 7x - 6x + 21 - 3 = 0
⇔ - 4x + 20 = 0
⇔ x = 5
10. (x - 5)(- x + 4) - (x - 1)(x + 3) = - 2x²
⇔ - x² + 4x + 5x - 20 - x² - 3x + x + 3 + 2x² = 0
⇔ 7x - 17 = 0
⇔ x = 17/7
11. (4x + 1)(x - 3) - (x - 7)(4x - 1) = 15
⇔ 4x² - 12x + x - 3 - 4x² + x + 28x - 7 - 15 = 0
⇔ 18x - 25 = 0
⇔ x = 25/18
12. (x + 1)(x² - x + 1) - x(x² - 3) = 4
⇔ x³ - x² + x + x² - x + 1 - x³ + 3x - 4 = 0
⇔ 3x - 3 = 0
⇔ x = 1
13. (x - 3)(x² + 3x + 9) + x(5 - x²) = 6x
⇔ x³ + 3x² + 9x - 3x² - 9x - 27 + 5x - x³ - 6x = 0
⇔ - x - 27 = 0
⇔ x = -27
14. (5x - 1)(5x + 1) = 25x² - 7x + 15
⇔ 25x² + 5x - 5x - 1 - 25x² + 7x - 15 = 0
⇔ 7x - 16 = 0
⇔ x = 16/7
15. 8x(x - 7) + 4x(x² - 5) = 28x² - 13
⇔ 8x² - 56x + 4x³ - 20x - 28x² + 13 = 0
⇔ 4x³ - 20x² - 76x +13 = 0
⇒ x = -2,645716723
x = 0,164191192
x = 7,481525531
16. (4x - 5)(x +1) - 4(x - 1)(x + 1) = 7
⇔ 4x² + 4x - 5x - 5 - 4x² - 4x + 4x + 4 - 7 = 0
⇔ - x - 8 = 0
⇔ x = - 8
17. (3x - 5)(x + 1) - (3x - 1)(x + 1) = x - 4
⇔ 3x² + 3x - 5x -5 - 3x² - 3x + x + 1 - x + 4 = 0
⇔ - 5x = 0
⇔ x = 0
18. (x - 2)(x + 3) - (x + 4)(x - 7) = 5 - x
⇔ x² + 3x - 2x - 6 - x² + 7x - 4x + 28 - 5 + x = 0
⇔ 5x + 17 = 0
⇔ x = -17/5
19. 5(x - 3)(x - 7) - (5x + 1)(x - 2) = 8
⇔ 5x² - 35x -15x + 105 - 5x² + 10x - x + 2 - 8 = 0
⇔ - 41x + 99 = 0
⇔ x = 99/41
20. 3(x - 7)(x + 7) - (x - 1)(3x + 2) = 13
⇔ 3x² + 21x - 21x - 147 - 3x² - 2x + 3x + 2 - 13 = 0
⇔ x - 158 = 0
⇔ x = 158
21. (2x - 3)(x + 1) - 2x(x - 5) = 9
⇔ 2x² + 2x - 3x - 3 - 2x² + 10x - 9 = 0
⇔ 9x - 12 = 0
⇔ x = 4/3
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