z2-z3=54

To write z2 as a fraction with a common denominator, multiply by 33.

z2⋅33-z3=54

To write -z3 as a fraction with a common denominator, multiply by 22.

z2⋅33-z3⋅22=54

Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.

Multiply z2 and 33.

z⋅32⋅3-z3⋅22=54

Multiply 2 by 3.

z⋅36-z3⋅22=54

Multiply z3 and 22.

z⋅36-z⋅23⋅2=54

Multiply 3 by 2.

z⋅36-z⋅26=54

z⋅36-z⋅26=54

Combine the numerators over the common denominator.

z⋅3-z⋅26=54

Simplify the numerator.

Factor z out of z⋅3-z⋅2.

Factor z out of z⋅3.

z(3)-z⋅26=54

Factor z out of -z⋅2.

z(3)+z(-1⋅2)6=54

Factor z out of z(3)+z(-1⋅2).

z(3-1⋅2)6=54

z(3-1⋅2)6=54

Multiply -1 by 2.

z(3-2)6=54

Subtract 2 from 3.

z⋅16=54

z⋅16=54

Multiply z by 1.

z6=54

z6=54

Multiply both sides of the equation by 6.

6⋅z6=6⋅54

Cancel the common factor of 6.

Cancel the common factor.

6⋅z6=6⋅54

Rewrite the expression.

z=6⋅54

z=6⋅54

Multiply 6 by 54.

z=324

z=324

Solve for z z/2-z/3=54