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5\times 5+5x\left(-\frac{1}{5}\right)=0
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x, the least common multiple of x,5.
25+5x\left(-\frac{1}{5}\right)=0
Multiply 5 and 5 to get 25.
25-x=0
Cancel out 5 and 5.
-x=-25
Subtract 25 from both sides. Anything subtracted from zero gives its negation.
x=25
Multiply both sides by -1.