# Solve for y 1/4*((3-1/7y)/2)-2/7y=-2

14⋅(3-17y2)-27y=-2
Factor the equation.
Simplify the numerator.
Combine y and 17.
14⋅3-y72-27y=-2
To write 3 as a fraction with a common denominator, multiply by 77.
14⋅3⋅77-y72-27y=-2
Combine 3 and 77.
14⋅3⋅77-y72-27y=-2
Combine the numerators over the common denominator.
14⋅3⋅7-y72-27y=-2
Multiply 3 by 7.
14⋅21-y72-27y=-2
14⋅21-y72-27y=-2
Multiply the numerator by the reciprocal of the denominator.
14⋅(21-y7⋅12)-27y=-2
Multiply 21-y7⋅12.
Multiply 21-y7 and 12.
14⋅21-y7⋅2-27y=-2
Multiply 7 by 2.
14⋅21-y14-27y=-2
14⋅21-y14-27y=-2
Multiply 14⋅21-y14.
Multiply 14 and 21-y14.
21-y4⋅14-27y=-2
Multiply 4 by 14.
21-y56-27y=-2
21-y56-27y=-2
Combine y and 27.
21-y56-y⋅27=-2
Move 2 to the left of y.
21-y56-2⋅y7=-2
Multiply 2 by y.
21-y56-2y7=-2
To write -2y7 as a fraction with a common denominator, multiply by 88.
21-y56-2y7⋅88=-2
Write each expression with a common denominator of 56, by multiplying each by an appropriate factor of 1.
Multiply 2y7 and 88.
21-y56-2y⋅87⋅8=-2
Multiply 7 by 8.
21-y56-2y⋅856=-2
21-y56-2y⋅856=-2
Combine the numerators over the common denominator.
21-y-2y⋅856=-2
Rewrite 21-y-2y⋅856 in a factored form.
Multiply 8 by -2.
21-y-16y56=-2
Subtract 16y from -y.
21-17y56=-2
21-17y56=-2
21-17y56=-2
Solve the equation.
Multiply both sides of the equation by 56.
21-17y=-2⋅56
Remove parentheses.
21-17y=-2⋅56
Multiply -2 by 56.
21-17y=-112
Move all terms not containing y to the right side of the equation.
Subtract 21 from both sides of the equation.
-17y=-112-21
Subtract 21 from -112.
-17y=-133
-17y=-133
Divide each term by -17 and simplify.
Divide each term in -17y=-133 by -17.
-17y-17=-133-17
Cancel the common factor of -17.
Cancel the common factor.
-17y-17=-133-17
Divide y by 1.
y=-133-17
y=-133-17
Dividing two negative values results in a positive value.
y=13317
y=13317
y=13317
The result can be shown in multiple forms.
Exact Form:
y=13317
Decimal Form:
y=7.82352941…
Mixed Number Form:
y=71417
Solve for y 1/4*((3-1/7y)/2)-2/7y=-2

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