# Solve for n (4n)/5+1/5=-9/10

4n5+15=-910
Move all terms not containing n to the right side of the equation.
Subtract 15 from both sides of the equation.
4n5=-910-15
To write -15 as a fraction with a common denominator, multiply by 22.
4n5=-910-15⋅22
Write each expression with a common denominator of 10, by multiplying each by an appropriate factor of 1.
Multiply 15 and 22.
4n5=-910-25⋅2
Multiply 5 by 2.
4n5=-910-210
4n5=-910-210
Combine the numerators over the common denominator.
4n5=-9-210
Subtract 2 from -9.
4n5=-1110
Move the negative in front of the fraction.
4n5=-1110
4n5=-1110
Multiply both sides of the equation by 54.
54⋅4n5=54⋅(-1110)
Simplify both sides of the equation.
Simplify 54⋅4n5.
Cancel the common factor of 5.
Cancel the common factor.
54⋅4n5=54⋅(-1110)
Rewrite the expression.
14⋅(4n)=54⋅(-1110)
14⋅(4n)=54⋅(-1110)
Cancel the common factor of 4.
Factor 4 out of 4n.
14⋅(4(n))=54⋅(-1110)
Cancel the common factor.
14⋅(4n)=54⋅(-1110)
Rewrite the expression.
n=54⋅(-1110)
n=54⋅(-1110)
n=54⋅(-1110)
Simplify 54⋅(-1110).
Cancel the common factor of 5.
Move the leading negative in -1110 into the numerator.
n=54⋅-1110
Factor 5 out of 10.
n=54⋅-115(2)
Cancel the common factor.
n=54⋅-115⋅2
Rewrite the expression.
n=14⋅-112
n=14⋅-112
Multiply 14 and -112.
n=-114⋅2
Simplify the expression.
Multiply 4 by 2.
n=-118
Move the negative in front of the fraction.
n=-118
n=-118
n=-118
n=-118
The result can be shown in multiple forms.
Exact Form:
n=-118
Decimal Form:
n=-1.375
Mixed Number Form:
n=-138
Solve for n (4n)/5+1/5=-9/10