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

13y-14⋅(y-1)=3y
Simplify 13y-14⋅(y-1).
Simplify each term.
Combine 13 and y.
y3-14⋅(y-1)=3y
Apply the distributive property.
y3-14y-14⋅-1=3y
Combine y and 14.
y3-y4-14⋅-1=3y
Multiply -14⋅-1.
Multiply -1 by -1.
y3-y4+1(14)=3y
Multiply 14 by 1.
y3-y4+14=3y
y3-y4+14=3y
y3-y4+14=3y
To write y3 as a fraction with a common denominator, multiply by 44.
y3⋅44-y4+14=3y
To write -y4 as a fraction with a common denominator, multiply by 33.
y3⋅44-y4⋅33+14=3y
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
Multiply y3 and 44.
y⋅43⋅4-y4⋅33+14=3y
Multiply 3 by 4.
y⋅412-y4⋅33+14=3y
Multiply y4 and 33.
y⋅412-y⋅34⋅3+14=3y
Multiply 4 by 3.
y⋅412-y⋅312+14=3y
y⋅412-y⋅312+14=3y
Combine the numerators over the common denominator.
y⋅4-y⋅312+14=3y
Simplify each term.
Simplify the numerator.
Factor y out of y⋅4-y⋅3.
Factor y out of y⋅4.
y(4)-y⋅312+14=3y
Factor y out of -y⋅3.
y(4)+y(-1⋅3)12+14=3y
Factor y out of y(4)+y(-1⋅3).
y(4-1⋅3)12+14=3y
y(4-1⋅3)12+14=3y
Multiply -1 by 3.
y(4-3)12+14=3y
Subtract 3 from 4.
y⋅112+14=3y
y⋅112+14=3y
Multiply y by 1.
y12+14=3y
y12+14=3y
y12+14=3y
Move all terms containing y to the left side of the equation.
Subtract 3y from both sides of the equation.
y12+14-3y=0
To write -3y as a fraction with a common denominator, multiply by 1212.
y12-3y⋅1212+14=0
Combine -3y and 1212.
y12+-3y⋅1212+14=0
Combine the numerators over the common denominator.
y-3y⋅1212+14=0
Simplify each term.
Simplify the numerator.
Factor y out of y-3y⋅12.
Raise y to the power of 1.
y1-3y⋅1212+14=0
Factor y out of y1.
y⋅1-3y⋅1212+14=0
Factor y out of -3y⋅12.
y⋅1+y(-3⋅12)12+14=0
Factor y out of y⋅1+y(-3⋅12).
y(1-3⋅12)12+14=0
y(1-3⋅12)12+14=0
Multiply -3 by 12.
y(1-36)12+14=0
Subtract 36 from 1.
y⋅-3512+14=0
y⋅-3512+14=0
Move -35 to the left of y.
-35⋅y12+14=0
Move the negative in front of the fraction.
-35y12+14=0
-35y12+14=0
-35y12+14=0
Subtract 14 from both sides of the equation.
-35y12=-14
Multiply both sides of the equation by -1235.
-1235⋅(-35y12)=-1235⋅(-14)
Simplify both sides of the equation.
Simplify -1235⋅(-35y12).
Cancel the common factor of 12.
Move the leading negative in -1235 into the numerator.
-1235⋅(-35y12)=-1235⋅(-14)
Move the leading negative in -35y12 into the numerator.
-1235⋅-35y12=-1235⋅(-14)
Factor 12 out of -12.
12(-1)35⋅-35y12=-1235⋅(-14)
Cancel the common factor.
12⋅-135⋅-35y12=-1235⋅(-14)
Rewrite the expression.
-135⋅(-35y)=-1235⋅(-14)
-135⋅(-35y)=-1235⋅(-14)
Cancel the common factor of 35.
Factor 35 out of -35y.
-135⋅(35(-y))=-1235⋅(-14)
Cancel the common factor.
-135⋅(35(-y))=-1235⋅(-14)
Rewrite the expression.
-1⋅(-y)=-1235⋅(-14)
-1⋅(-y)=-1235⋅(-14)
Multiply.
Multiply -1 by -1.
1⋅y=-1235⋅(-14)
Multiply y by 1.
y=-1235⋅(-14)
y=-1235⋅(-14)
y=-1235⋅(-14)
Simplify -1235⋅(-14).
Cancel the common factor of 4.
Move the leading negative in -1235 into the numerator.
y=-1235⋅(-14)
Move the leading negative in -14 into the numerator.
y=-1235⋅-14
Factor 4 out of -12.
y=4(-3)35⋅-14
Cancel the common factor.
y=4⋅-335⋅-14
Rewrite the expression.
y=-335⋅-1
y=-335⋅-1
Combine -335 and -1.
y=-3⋅-135
Multiply -3 by -1.
y=335
y=335
y=335
The result can be shown in multiple forms.
Exact Form:
y=335
Decimal Form:
y=0.0857142‾
Solve for y 1/3y-1/4*(y-1)=3y

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