1) Решение уравнения 2x^2 - x(2x - 5) - 2(2x - 1) - 5 = 0:
2x^2 - 2x^2 + 5x - 4x + 4 - 2 - 5 = 0
x - 3 = 0
x = 3

2) Решение уравнения 6x(x + 2) - 0.5(12x^2 - 7x) - 31 = 0:
6x^2 + 12x - 6x^2 + 3.5x - 31 = 0
3.5x + 12 - 31 = 0
3.5x - 19 = 0
x = 19/3.5 = 5.428571

3) Решение уравнения 12x(x - 8) - 4x(3x - 5) = 10 - 26x:
12x^2 - 96x - 12x^2 + 20x = 10 - 26x
-76x = 10 - 26x
50x = 10
x = 10/50 = 0.2

4) Решение уравнения 8(x^2 - 5) - 5x(x + 8) = 3x^2 - 11x + 18:
8x^2 - 40 - 5x^2 - 40x = 3x^2 - 11x + 18
3x^2 - 40x - 40 = 3x^2 - 11x + 18
-29x - 40 = -11x + 18
-18 - 40 = 18 - 11x + 29x
-58 = 18 + 18x
-58 = 18(1 + x)
x = (-58 - 18)/18 = -4