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12\times 7=z\times 84
Variable z cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12z, the least common multiple of z,12.
84=z\times 84
Multiply 12 and 7 to get 84.
z\times 84=84
Swap sides so that all variable terms are on the left hand side.
z=\frac{84}{84}
Divide both sides by 84.
z=1
Divide 84 by 84 to get 1.