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4-3(z+2)=5z+1
We move all terms to the left:
4-3(z+2)-(5z+1)=0
We multiply parentheses
-3z-(5z+1)-6+4=0
We get rid of parentheses
-3z-5z-1-6+4=0
We add all the numbers together, and all the variables
-8z-3=0
We move all terms containing z to the left, all other terms to the right
-8z=3
z=3/-8
z=-3/8
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