What is the answer to ((5y-6)(4y-8))/(5y-2)=4y+5 ?

The answer to ((5y-6)(4y-8))/(5y-2)=4y+5 is y= 58/81

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((5y-6)(4y-8))/(5y-2)=4y+5

\frac{( 5 y - 6 ) ( 4 y - 8 )}{5 y - 2} = 4 y + 5

y = \frac{58}{81}

Solution steps

\frac{( 5 y - 6 ) ( 4 y - 8 )}{5 y - 2} = 4 y + 5

Multiply both sides by

5 y - 2

(5 y - 6) (4 y - 8) = 4 y (5 y - 2) + 5 (5 y - 2)

Expand

4 y (5 y - 2) : 20 y^{2} - 8 y

20 y^{2} - 64 y + 48 = 20 y^{2} - 8 y + 5 (5 y - 2)

Expand

5 (5 y - 2) : 25 y - 10

20 y^{2} - 64 y + 48 = 20 y^{2} - 8 y + 25 y - 10

Add similar elements:

- 8 y + 25 y = 17 y

20 y^{2} - 64 y + 48 = 20 y^{2} + 17 y - 10

Expand

(5 y - 6) (4 y - 8) : 20 y^{2} - 64 y + 48

20 y^{2} - 64 y + 48 = 20 y^{2} + 17 y - 10

Move

48

to the right side

20 y^{2} - 64 y = 20 y^{2} + 17 y - 58

Subtract

20 y^{2} + 17 y

from both sides

20 y^{2} - 64 y - (20 y^{2} + 17 y) = 20 y^{2} + 17 y - 58 - (20 y^{2} + 17 y)

Simplify

- 81 y = - 58

Divide both sides by

- 81

y = \frac{58}{81}

Verify Solutions

Find undefined (singularity) points:

y = \frac{2}{5}

Combine undefined points with solutions:

y = \frac{58}{81}

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What is the answer to ((5y-6)(4y-8))/(5y-2)=4y+5 ?
The answer to ((5y-6)(4y-8))/(5y-2)=4y+5 is y= 58/81
Solve for y: ((5y-6)(4y-8))/(5y-2)=4y+5
The solution is y= 58/81