4. Найдите корни уравнения: a) (10x + 30)(2x - 50) = 0 б) (15x - 45)(3x + 75) = 0 в) (25x - 75)(5x + 125) = 0 г) (7x - 21)(x + 35) = 0 д) (14x + 42)(2x - 70) = 0 e) (x - 63)(x - 57) = 0 ж) (8x - 64)(x + 71) = 0 з) (24 - x)(x + 67) = 0

Решение:

1. a) (10x + 30)(2x - 50) = 0
   \( 10x + 30 = 0 \) \( \Rightarrow 10x = -30 \) \( \Rightarrow x = -3 \)
   \( 2x - 50 = 0 \) \( \Rightarrow 2x = 50 \) \( \Rightarrow x = 25 \)
2. б) (15x - 45)(3x + 75) = 0
   \( 15x - 45 = 0 \) \( \Rightarrow 15x = 45 \) \( \Rightarrow x = 3 \)
   \( 3x + 75 = 0 \) \( \Rightarrow 3x = -75 \) \( \Rightarrow x = -25 \)
3. в) (25x - 75)(5x + 125) = 0
   \( 25x - 75 = 0 \) \( \Rightarrow 25x = 75 \) \( \Rightarrow x = 3 \)
   \( 5x + 125 = 0 \) \( \Rightarrow 5x = -125 \) \( \Rightarrow x = -25 \)
4. г) (7x - 21)(x + 35) = 0
   \( 7x - 21 = 0 \) \( \Rightarrow 7x = 21 \) \( \Rightarrow x = 3 \)
   \( x + 35 = 0 \) \( \Rightarrow x = -35 \)
5. д) (14x + 42)(2x - 70) = 0
   \( 14x + 42 = 0 \) \( \Rightarrow 14x = -42 \) \( \Rightarrow x = -3 \)
   \( 2x - 70 = 0 \) \( \Rightarrow 2x = 70 \) \( \Rightarrow x = 35 \)
6. е) (x - 63)(x - 57) = 0
   \( x - 63 = 0 \) \( \Rightarrow x = 63 \)
   \( x - 57 = 0 \) \( \Rightarrow x = 57 \)
7. ж) (8x - 64)(x + 71) = 0
   \( 8x - 64 = 0 \) \( \Rightarrow 8x = 64 \) \( \Rightarrow x = 8 \)
   \( x + 71 = 0 \) \( \Rightarrow x = -71 \)
8. з) (24 - x)(x + 67) = 0
   \( 24 - x = 0 \) \( \Rightarrow x = 24 \)
   \( x + 67 = 0 \) \( \Rightarrow x = -67 \)

Ответ: а) -3; 25; б) 3; -25; в) 3; -25; г) 3; -35; д) -3; 35; е) 63; 57; ж) 8; -71; з) 24; -67.