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32=5^3x+1
We move all terms to the left:
32-(5^3x+1)=0
We get rid of parentheses
-5^3x-1+32=0
We add all the numbers together, and all the variables
-5^3x+31=0
We move all terms containing x to the left, all other terms to the right
-5^3x=-31
x=-31/1
x=-31
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