y-(7-8y)/9y-(3+4y)=2/3

To solve the given equation: y - (7 - 8y)/(9y) - (3 + 4y) = 2/3, we can follow these steps:

Step 1: Simplify the expression inside the parentheses.
- Distribute the negative sign to the terms inside the parentheses:
y - (7 - 8y)/(9y) - 3 - 4y = 2/3

- Simplify the expression inside the first parentheses:
y - (7 - 8y)/(9y) can be rewritten as y + (-1*(7 - 8y))/(9y)
Now, distribute the -1 to the terms inside the parentheses:
y - (7 - 8y)/(9y) = y + (-1*7 + 1*8y)/(9y) = y + (-7 + 8y)/(9y)

Step 2: Combine like terms.
y + (-7 + 8y)/(9y) - 3 - 4y = 2/3
Simplify (-7 + 8y)/(9y):
(-7 + 8y)/(9y) can be expressed as (-7/9y) + (8y/9y)
(-7 + 8y)/(9y) = (-7/9y) + (8y/9y) = (8y - 7)/(9y)

Step 3: Substitute the simplified expression back into the equation.
y + (8y - 7)/(9y) - 3 - 4y = 2/3

Step 4: Combine like terms on both sides of the equation.
On the left side:
y + (8y - 7)/(9y) - 3 - 4y can be simplified as:
(y - 4y) + (8y - 7)/(9y) - 3 = -3y + (8y - 7)/(9y) - 3

On the right side:
2/3 remains the same.

Now, the equation becomes:
-3y + (8y - 7)/(9y) - 3 = 2/3

Step 5: Clear the fractions.
Multiply both sides of the equation by the common denominator, which is 9y:
(9y)*(-3y + (8y - 7)/(9y) - 3) = (9y)*(2/3)

Simplify:
-27y^2 + 8y - 7 - 27y = 6y

Step 6: Rearrange the equation to bring all terms to one side and simplify.
-27y^2 + 8y - 7 - 27y - 6y = 0

Group the like terms:
-27y^2 - 25y - 7 = 0

Now, the quadratic equation -27y^2 - 25y - 7 = 0 is obtained. You can proceed to solve this equation using various methods such as factoring, completing the square, or using the quadratic formula.