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7-6z=-8z-7
We move all terms to the left:
7-6z-(-8z-7)=0
We get rid of parentheses
-6z+8z+7+7=0
We add all the numbers together, and all the variables
2z+14=0
We move all terms containing z to the left, all other terms to the right
2z=-14
z=-14/2
z=-7
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