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5x-6=-3x+9
We move all terms to the left:
5x-6-(-3x+9)=0
We get rid of parentheses
5x+3x-9-6=0
We add all the numbers together, and all the variables
8x-15=0
We move all terms containing x to the left, all other terms to the right
8x=15
x=15/8
x=1+7/8
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