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5z+2(z-4)=13
We move all terms to the left:
5z+2(z-4)-(13)=0
We multiply parentheses
5z+2z-8-13=0
We add all the numbers together, and all the variables
7z-21=0
We move all terms containing z to the left, all other terms to the right
7z=21
z=21/7
z=3
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