# Solve for y -3/2y-2=1/3y-5/6

-32y-2=13y-56
Simplify each term.
Combine y and 32.
-y⋅32-2=13y-56
Move 3 to the left of y.
-3y2-2=13y-56
-3y2-2=13y-56
Combine 13 and y.
-3y2-2=y3-56
Move all terms containing y to the left side of the equation.
Subtract y3 from both sides of the equation.
-3y2-2-y3=-56
To write -3y2 as a fraction with a common denominator, multiply by 33.
-3y2⋅33-y3-2=-56
To write -y3 as a fraction with a common denominator, multiply by 22.
-3y2⋅33-y3⋅22-2=-56
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply 3y2 and 33.
-3y⋅32⋅3-y3⋅22-2=-56
Multiply 2 by 3.
-3y⋅36-y3⋅22-2=-56
Multiply y3 and 22.
-3y⋅36-y⋅23⋅2-2=-56
Multiply 3 by 2.
-3y⋅36-y⋅26-2=-56
-3y⋅36-y⋅26-2=-56
Combine the numerators over the common denominator.
-3y⋅3-y⋅26-2=-56
Simplify each term.
Simplify the numerator.
Factor y out of -3y⋅3-y⋅2.
Factor y out of -3y⋅3.
y(-3⋅3)-y⋅26-2=-56
Factor y out of -y⋅2.
y(-3⋅3)+y(-1⋅2)6-2=-56
Factor y out of y(-3⋅3)+y(-1⋅2).
y(-3⋅3-1⋅2)6-2=-56
y(-3⋅3-1⋅2)6-2=-56
Multiply -3 by 3.
y(-9-1⋅2)6-2=-56
Multiply -1 by 2.
y(-9-2)6-2=-56
Subtract 2 from -9.
y⋅-116-2=-56
y⋅-116-2=-56
Move -11 to the left of y.
-11⋅y6-2=-56
Move the negative in front of the fraction.
-11y6-2=-56
-11y6-2=-56
-11y6-2=-56
Move all terms not containing y to the right side of the equation.
Add 2 to both sides of the equation.
-11y6=-56+2
To write 2 as a fraction with a common denominator, multiply by 66.
-11y6=-56+2⋅66
Combine 2 and 66.
-11y6=-56+2⋅66
Combine the numerators over the common denominator.
-11y6=-5+2⋅66
Simplify the numerator.
Multiply 2 by 6.
-11y6=-5+126
Add -5 and 12.
-11y6=76
-11y6=76
-11y6=76
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
-11y=7
Divide each term by -11 and simplify.
Divide each term in -11y=7 by -11.
-11y-11=7-11
Cancel the common factor of -11.
Cancel the common factor.
-11y-11=7-11
Divide y by 1.
y=7-11
y=7-11
Move the negative in front of the fraction.
y=-711
y=-711
The result can be shown in multiple forms.
Exact Form:
y=-711
Decimal Form:
y=-0.63‾
Solve for y -3/2y-2=1/3y-5/6

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