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20\left(0\times 100-x\right)+30x=0
Multiply both sides by 80. Anything times zero gives zero.
20\left(0-x\right)+30x=0
Multiply 0 and 100 to get 0.
20\left(-1\right)x+30x=0
Anything plus zero gives itself.
-20x+30x=0
Multiply 20 and -1 to get -20.
10x=0
Combine -20x and 30x to get 10x.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since 10 is not equal to 0, x must be equal to 0.