To solve each equation, we will isolate the variable x.

a) 4/9(x - 1) = 0
First, distribute the 4/9 to the terms inside the parentheses:
4/9 * x - 4/9 * 1 = 0
4x/9 - 4/9 = 0
Combine like terms:
4x/9 - 4/9 = 0
4x - 4 = 0
Add 4 to both sides:
4x = 4
Divide both sides by 4:
x = 1

b) x(2x - 4/11) = 0
To solve this equation, we can use the zero product property, which states that if a product of two factors is equal to zero, then at least one of the factors must be zero.
So, either x = 0 or 2x - 4/11 = 0.
If 2x - 4/11 = 0, add 4/11 to both sides:
2x = 4/11
Divide both sides by 2:
x = 4/22
Simplify the fraction:
x = 2/11

c) -2x(2x + 6/7) = 0
Again, we can use the zero product property.
Either -2x = 0 or 2x + 6/7 = 0.
If 2x + 6/7 = 0, subtract 6/7 from both sides:
2x = -6/7
Divide both sides by 2:
x = -6/14
Simplify the fraction:
x = -3/7

d) -11/29 x(5/7 - x) = 0
Once again, we can use the zero product property.
Either -11/29 x = 0 or 5/7 - x = 0.
If 5/7 - x = 0, add x to both sides:
5/7 = x
If -11/29 x = 0, then x = 0.
So, the solutions are x = 0 and x = 5/7.