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9x+6=-3x-6
We move all terms to the left:
9x+6-(-3x-6)=0
We get rid of parentheses
9x+3x+6+6=0
We add all the numbers together, and all the variables
12x+12=0
We move all terms containing x to the left, all other terms to the right
12x=-12
x=-12/12
x=-1
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