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3+2z=-2z+7
We move all terms to the left:
3+2z-(-2z+7)=0
We get rid of parentheses
2z+2z-7+3=0
We add all the numbers together, and all the variables
4z-4=0
We move all terms containing z to the left, all other terms to the right
4z=4
z=4/4
z=1
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