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

Math
12n+10=-14n+54
Combine 12 and n.
n2+10=-14n+54
Combine n and 14.
n2+10=-n4+54
Move all terms containing n to the left side of the equation.
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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.
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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.
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Reorder n and 2.
2⋅n+n4+10=54
Add 2⋅n and n.
3⋅n4+10=54
3n4+10=54
3n4+10=54
Move all terms not containing n to the right side of the equation.
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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 both sides of the equation.
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Simplify 43⋅3n4.
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Cancel the common factor of 4.
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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.
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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.
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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

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