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-6(z-7)+7z=-1
We move all terms to the left:
-6(z-7)+7z-(-1)=0
We add all the numbers together, and all the variables
7z-6(z-7)+1=0
We multiply parentheses
7z-6z+42+1=0
We add all the numbers together, and all the variables
z+43=0
We move all terms containing z to the left, all other terms to the right
z=-43
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