# Solve for y (2y+3)/4+(y-5)/6=0

2y+34+y-56=0
Factor the equation.
To write 2y+34 as a fraction with a common denominator, multiply by 33.
2y+34⋅33+y-56=0
To write y-56 as a fraction with a common denominator, multiply by 22.
2y+34⋅33+y-56⋅22=0
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
Multiply 2y+34 and 33.
(2y+3)⋅34⋅3+y-56⋅22=0
Multiply 4 by 3.
(2y+3)⋅312+y-56⋅22=0
Multiply y-56 and 22.
(2y+3)⋅312+(y-5)⋅26⋅2=0
Multiply 6 by 2.
(2y+3)⋅312+(y-5)⋅212=0
(2y+3)⋅312+(y-5)⋅212=0
Combine the numerators over the common denominator.
(2y+3)⋅3+(y-5)⋅212=0
Rewrite (2y+3)⋅3+(y-5)⋅212 in a factored form.
Apply the distributive property.
2y⋅3+3⋅3+(y-5)⋅212=0
Multiply 3 by 2.
6y+3⋅3+(y-5)⋅212=0
Multiply 3 by 3.
6y+9+(y-5)⋅212=0
Apply the distributive property.
6y+9+y⋅2-5⋅212=0
Move 2 to the left of y.
6y+9+2⋅y-5⋅212=0
Multiply -5 by 2.
6y+9+2y-1012=0
8y+9-1012=0
Subtract 10 from 9.
8y-112=0
8y-112=0
8y-112=0
Solve the equation.
Multiply both sides of the equation by 12.
8y-1=0⋅(12)
Remove parentheses.
8y-1=0⋅(12)
Multiply 0 by 12.
8y-1=0
Add 1 to both sides of the equation.
8y=1
Divide each term by 8 and simplify.
Divide each term in 8y=1 by 8.
8y8=18
Cancel the common factor of 8.
Cancel the common factor.
8y8=18
Divide y by 1.
y=18
y=18
y=18
y=18
The result can be shown in multiple forms.
Exact Form:
y=18
Decimal Form:
y=0.125
Solve for y (2y+3)/4+(y-5)/6=0

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