5n8-12=34

Add 12 to both sides of the equation.

5n8=34+12

To write 12 as a fraction with a common denominator, multiply by 22.

5n8=34+12⋅22

Write each expression with a common denominator of 4, by multiplying each by an appropriate factor of 1.

Multiply 12 and 22.

5n8=34+22⋅2

Multiply 2 by 2.

5n8=34+24

5n8=34+24

Combine the numerators over the common denominator.

5n8=3+24

Add 3 and 2.

5n8=54

5n8=54

Multiply both sides of the equation by 85.

85⋅5n8=85⋅54

Simplify 85⋅5n8.

Cancel the common factor of 8.

Cancel the common factor.

85⋅5n8=85⋅54

Rewrite the expression.

15⋅(5n)=85⋅54

15⋅(5n)=85⋅54

Cancel the common factor of 5.

Factor 5 out of 5n.

15⋅(5(n))=85⋅54

Cancel the common factor.

15⋅(5n)=85⋅54

Rewrite the expression.

n=85⋅54

n=85⋅54

n=85⋅54

Simplify 85⋅54.

Cancel the common factor of 4.

Factor 4 out of 8.

n=4(2)5⋅54

Cancel the common factor.

n=4⋅25⋅54

Rewrite the expression.

n=25⋅5

n=25⋅5

Cancel the common factor of 5.

Cancel the common factor.

n=25⋅5

Rewrite the expression.

n=2

n=2

n=2

n=2

Solve for n (5n)/8-1/2=3/4