# Solve for y 2(1/2y+1)=-3(2y-1)+4(2y+1) 2(12y+1)=-3(2y-1)+4(2y+1)
Since y is on the right side of the equation, switch the sides so it is on the left side of the equation.
-3(2y-1)+4(2y+1)=2(12y+1)
Simplify -3(2y-1)+4(2y+1).
Simplify each term.
Apply the distributive property.
-3(2y)-3⋅-1+4(2y+1)=2(12y+1)
Multiply 2 by -3.
-6y-3⋅-1+4(2y+1)=2(12y+1)
Multiply -3 by -1.
-6y+3+4(2y+1)=2(12y+1)
Apply the distributive property.
-6y+3+4(2y)+4⋅1=2(12y+1)
Multiply 2 by 4.
-6y+3+8y+4⋅1=2(12y+1)
Multiply 4 by 1.
-6y+3+8y+4=2(12y+1)
-6y+3+8y+4=2(12y+1)
Simplify by adding terms.
Add -6y and 8y.
2y+3+4=2(12y+1)
Add 3 and 4.
2y+7=2(12y+1)
2y+7=2(12y+1)
2y+7=2(12y+1)
Simplify 2(12y+1).
Combine 12 and y.
2y+7=2(y2+1)
Apply the distributive property.
2y+7=2y2+2⋅1
Cancel the common factor of 2.
Cancel the common factor.
2y+7=2y2+2⋅1
Rewrite the expression.
2y+7=y+2⋅1
2y+7=y+2⋅1
Multiply 2 by 1.
2y+7=y+2
2y+7=y+2
Move all terms containing y to the left side of the equation.
Subtract y from both sides of the equation.
2y+7-y=2
Subtract y from 2y.
y+7=2
y+7=2
Move all terms not containing y to the right side of the equation.
Subtract 7 from both sides of the equation.
y=2-7
Subtract 7 from 2.
y=-5
y=-5
Solve for y 2(1/2y+1)=-3(2y-1)+4(2y+1)

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