-8(z+14)+9=10(z-11)

1. Distribute the constants inside the parentheses:
-8z - 112 + 9 = 10z - 110

2. Simplify both sides:
-8z - 103 = 10z - 110

3. Move the z terms to one side by adding 8z to both sides:
-103 = 18z - 110

4. Isolate the z term by adding 110 to both sides:
7 = 18z

5. Solve for z by dividing both sides by 18:
z = \frac{7}{18}