Solve for y y/(7y-2)=(3y)/(13y-4)

Math
y7y-2=3y13y-4
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
y⋅(13y-4)=(7y-2)⋅(3y)
Solve the equation for y.
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Simplify y⋅(13y-4).
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Simplify by multiplying through.
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Apply the distributive property.
y(13y)+y⋅-4=(7y-2)⋅(3y)
Reorder.
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Rewrite using the commutative property of multiplication.
13y⋅y+y⋅-4=(7y-2)⋅(3y)
Move -4 to the left of y.
13y⋅y-4⋅y=(7y-2)⋅(3y)
13y⋅y-4⋅y=(7y-2)⋅(3y)
13y⋅y-4⋅y=(7y-2)⋅(3y)
Multiply y by y by adding the exponents.
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Move y.
13(y⋅y)-4⋅y=(7y-2)⋅(3y)
Multiply y by y.
13y2-4⋅y=(7y-2)⋅(3y)
13y2-4y=(7y-2)⋅(3y)
13y2-4y=(7y-2)⋅(3y)
Simplify (7y-2)⋅(3y).
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Apply the distributive property.
13y2-4y=7y(3y)-2(3y)
Simplify the expression.
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Multiply y by y.
13y2-4y=7⋅3y2-2(3y)
Multiply 3 by -2.
13y2-4y=7⋅3y2-6y
Multiply 7 by 3.
13y2-4y=21y2-6y
13y2-4y=21y2-6y
13y2-4y=21y2-6y
Move all terms containing y to the left side of the equation.
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Subtract 21y2 from both sides of the equation.
13y2-4y-21y2=-6y
Add 6y to both sides of the equation.
13y2-4y-21y2+6y=0
Subtract 21y2 from 13y2.
-8y2-4y+6y=0
Add -4y and 6y.
-8y2+2y=0
-8y2+2y=0
Factor -2y out of -8y2+2y.
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Factor -2y out of -8y2.
-2y(4y)+2y=0
Factor -2y out of 2y.
-2y(4y)-2y⋅-1=0
Factor -2y out of -2y(4y)-2y(-1).
-2y(4y-1)=0
-2y(4y-1)=0
Divide each term by -2 and simplify.
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Divide each term in -2y(4y-1)=0 by -2.
-2y(4y-1)-2=0-2
Simplify -2y(4y-1)-2.
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Simplify terms.
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Cancel the common factor of -2.
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Cancel the common factor.
-2y(4y-1)-2=0-2
Divide y(4y-1) by 1.
y(4y-1)=0-2
y(4y-1)=0-2
Apply the distributive property.
y(4y)+y⋅-1=0-2
Reorder.
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Rewrite using the commutative property of multiplication.
4y⋅y+y⋅-1=0-2
Move -1 to the left of y.
4y⋅y-1⋅y=0-2
4y⋅y-1⋅y=0-2
4y⋅y-1⋅y=0-2
Simplify each term.
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Multiply y by y by adding the exponents.
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Move y.
4(y⋅y)-1⋅y=0-2
Multiply y by y.
4y2-1⋅y=0-2
4y2-1⋅y=0-2
Rewrite -1y as -y.
4y2-y=0-2
4y2-y=0-2
4y2-y=0-2
Divide 0 by -2.
4y2-y=0
4y2-y=0
Factor y out of 4y2-y.
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Factor y out of 4y2.
y(4y)-y=0
Factor y out of -y.
y(4y)+y⋅-1=0
Factor y out of y(4y)+y⋅-1.
y(4y-1)=0
y(4y-1)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
y=0
4y-1=0
Set the first factor equal to 0.
y=0
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
4y-1=0
Add 1 to both sides of the equation.
4y=1
Divide each term by 4 and simplify.
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Divide each term in 4y=1 by 4.
4y4=14
Cancel the common factor of 4.
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Cancel the common factor.
4y4=14
Divide y by 1.
y=14
y=14
y=14
y=14
The final solution is all the values that make y(4y-1)=0 true.
y=0,14
y=0,14
The result can be shown in multiple forms.
Exact Form:
y=0,14
Decimal Form:
y=0,0.25
Solve for y y/(7y-2)=(3y)/(13y-4)

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