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4y-9=6y+3
We move all terms to the left:
4y-9-(6y+3)=0
We get rid of parentheses
4y-6y-3-9=0
We add all the numbers together, and all the variables
-2y-12=0
We move all terms containing y to the left, all other terms to the right
-2y=12
y=12/-2
y=-6
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