12n+10=-14n+54

Combine 12 and n.

n2+10=-14n+54

Combine n and 14.

n2+10=-n4+54

Add n4 to both sides of the equation.

n2+10+n4=54

To write n2 as a fraction with a common denominator, multiply by 22.

n2⋅22+n4+10=54

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

Multiply n2 and 22.

n⋅22⋅2+n4+10=54

Multiply 2 by 2.

n⋅24+n4+10=54

n⋅24+n4+10=54

Combine the numerators over the common denominator.

n⋅2+n4+10=54

Add n⋅2 and n.

Reorder n and 2.

2⋅n+n4+10=54

Add 2⋅n and n.

3⋅n4+10=54

3n4+10=54

3n4+10=54

Subtract 10 from both sides of the equation.

3n4=54-10

Subtract 10 from 54.

3n4=44

3n4=44

Multiply both sides of the equation by 43.

43⋅3n4=43⋅44

Simplify 43⋅3n4.

Cancel the common factor of 4.

Cancel the common factor.

43⋅3n4=43⋅44

Rewrite the expression.

13⋅(3n)=43⋅44

13⋅(3n)=43⋅44

Cancel the common factor of 3.

Factor 3 out of 3n.

13⋅(3(n))=43⋅44

Cancel the common factor.

13⋅(3n)=43⋅44

Rewrite the expression.

n=43⋅44

n=43⋅44

n=43⋅44

Multiply 43⋅44.

Combine 43 and 44.

n=4⋅443

Multiply 4 by 44.

n=1763

n=1763

n=1763

The result can be shown in multiple forms.

Exact Form:

n=1763

Decimal Form:

n=58.6‾

Mixed Number Form:

n=5823

Solve for n 1/2n+10=-1/4n+54