z3+5=z7+1

Subtract z7 from both sides of the equation.

z3+5-z7=1

To write z3 as a fraction with a common denominator, multiply by 77.

z3⋅77-z7+5=1

To write -z7 as a fraction with a common denominator, multiply by 33.

z3⋅77-z7⋅33+5=1

Write each expression with a common denominator of 21, by multiplying each by an appropriate factor of 1.

Multiply z3 and 77.

z⋅73⋅7-z7⋅33+5=1

Multiply 3 by 7.

z⋅721-z7⋅33+5=1

Multiply z7 and 33.

z⋅721-z⋅37⋅3+5=1

Multiply 7 by 3.

z⋅721-z⋅321+5=1

z⋅721-z⋅321+5=1

Combine the numerators over the common denominator.

z⋅7-z⋅321+5=1

Simplify each term.

Simplify the numerator.

Factor z out of z⋅7-z⋅3.

Factor z out of z⋅7.

z(7)-z⋅321+5=1

Factor z out of -z⋅3.

z(7)+z(-1⋅3)21+5=1

Factor z out of z(7)+z(-1⋅3).

z(7-1⋅3)21+5=1

z(7-1⋅3)21+5=1

Multiply -1 by 3.

z(7-3)21+5=1

Subtract 3 from 7.

z⋅421+5=1

z⋅421+5=1

Move 4 to the left of z.

4z21+5=1

4z21+5=1

4z21+5=1

Subtract 5 from both sides of the equation.

4z21=1-5

Subtract 5 from 1.

4z21=-4

4z21=-4

Multiply both sides of the equation by 214.

214⋅4z21=214⋅-4

Simplify 214⋅4z21.

Cancel the common factor of 21.

Cancel the common factor.

214⋅4z21=214⋅-4

Rewrite the expression.

14⋅(4z)=214⋅-4

14⋅(4z)=214⋅-4

Cancel the common factor of 4.

Factor 4 out of 4z.

14⋅(4(z))=214⋅-4

Cancel the common factor.

14⋅(4z)=214⋅-4

Rewrite the expression.

z=214⋅-4

z=214⋅-4

z=214⋅-4

Simplify 214⋅-4.

Cancel the common factor of 4.

Factor 4 out of -4.

z=214⋅(4(-1))

Cancel the common factor.

z=214⋅(4⋅-1)

Rewrite the expression.

z=21⋅-1

z=21⋅-1

Multiply 21 by -1.

z=-21

z=-21

z=-21

Solve for z z/3+5=z/7+1