1) Simplifying the equation 3z - 14/2 = -1:

3z - 7 = -1
3z = 6
z = 2

2) Simplifying the equation 3n + 75/5 = 6n + 42/5:

3n + 15 = 6n + 8
15 = 3n + 8
7 = 3n
n = 7/3

3) Simplifying the equation 4/x - x + 8/2x = 5/6:

4/x - x + 4/x = 5/6
(4 + x^2 + 8) / x = 5/6
(x^2 + 12) / x = 5/6
6(x^2 + 12) = 5x
6x^2 + 72 = 5x
6x^2 - 5x + 72 = 0

Solving this quadratic equation for x would provide the value(s) that satisfy the equation.