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3z=4z+9
We move all terms to the left:
3z-(4z+9)=0
We get rid of parentheses
3z-4z-9=0
We add all the numbers together, and all the variables
-1z-9=0
We move all terms containing z to the left, all other terms to the right
-z=9
z=9/-1
z=-9
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