# Solve for y 2/3+3y=5y-2/15

23+3y=5y-215
Move all terms containing y to the left side of the equation.
Subtract 5y from both sides of the equation.
23+3y-5y=-215
Subtract 5y from 3y.
23-2y=-215
23-2y=-215
Move all terms not containing y to the right side of the equation.
Subtract 23 from both sides of the equation.
-2y=-215-23
To write -23 as a fraction with a common denominator, multiply by 55.
-2y=-215-23⋅55
Write each expression with a common denominator of 15, by multiplying each by an appropriate factor of 1.
Multiply 23 and 55.
-2y=-215-2⋅53⋅5
Multiply 3 by 5.
-2y=-215-2⋅515
-2y=-215-2⋅515
Combine the numerators over the common denominator.
-2y=-2-2⋅515
Simplify the numerator.
Multiply -2 by 5.
-2y=-2-1015
Subtract 10 from -2.
-2y=-1215
-2y=-1215
Cancel the common factor of -12 and 15.
Factor 3 out of -12.
-2y=3(-4)15
Cancel the common factors.
Factor 3 out of 15.
-2y=3⋅-43⋅5
Cancel the common factor.
-2y=3⋅-43⋅5
Rewrite the expression.
-2y=-45
-2y=-45
-2y=-45
Move the negative in front of the fraction.
-2y=-45
-2y=-45
Divide each term by -2 and simplify.
Divide each term in -2y=-45 by -2.
-2y-2=-45⋅(-12)
Cancel the common factor of -2.
Cancel the common factor.
-2y-2=-45⋅(-12)
Divide y by 1.
y=-45⋅(-12)
y=-45⋅(-12)
Simplify -45⋅(-12).
Cancel the common factor of 2.
Move the leading negative in -45 into the numerator.
y=-45⋅(-12)
Move the leading negative in -12 into the numerator.
y=-45⋅-12
Factor 2 out of -4.
y=2(-2)5⋅-12
Cancel the common factor.
y=2⋅-25⋅-12
Rewrite the expression.
y=-25⋅-1
y=-25⋅-1
Combine -25 and -1.
y=-2⋅-15
Multiply -2 by -1.
y=25
y=25
y=25
The result can be shown in multiple forms.
Exact Form:
y=25
Decimal Form:
y=0.4
Solve for y 2/3+3y=5y-2/15

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