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125\times 5=X\times 625
Variable X cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 125X, the least common multiple of X,125.
625=X\times 625
Multiply 125 and 5 to get 625.
X\times 625=625
Swap sides so that all variable terms are on the left hand side.
X=\frac{625}{625}
Divide both sides by 625.
X=1
Divide 625 by 625 to get 1.