solve y; =6/y+2-4=y+20/3y+6

could someone help with this problem.

6/y+2-4=y+20/3y+6

Multiply by 3y.

18 + 6y - 12y = 3 + 20 + 18y

Combine y terms and numerical terms

-5 = 24y

Do you think you can take it from there?

is -5=24y

y=-5/24
let me know if this right answer

To solve the equation "y; =6/y+2-4=y+20/3y+6," we need to simplify and rearrange the equation to isolate the variable y. Let's go step by step:

Step 1: Simplify the right-hand side of the equation:
We can start by combining like terms on the right-hand side. The equation becomes:
y; = 6/(y + 2) - 4 = y + 20/(3y + 6)

Step 2: Clear fractions:
To clear the fractions, we'll multiply both sides of the equation by the least common denominator, which is (y + 2)(3y + 6). This helps us remove the denominators in the equation.

The equation becomes:
(y + 2)(3y + 6) * y; = (y + 2)(3y + 6) * (6/(y + 2)) - 4 * (y + 2)(3y + 6) = (y + 2)(3y + 6) * y + (y + 2)(3y + 6) * (20/(3y + 6))

Step 3: Distribute and simplify:
Distribute the terms on the right-hand side and simplify where possible:
(3y + 6) * y; = 6(y + 2) - 4(y + 2)(3y + 6) = y(3y + 6) + 2(3y + 6) - 4(y + 2)(3y + 6) = 3y^2 + 6y + 6y + 12 - 12y^2 - 24y - 72 = 3y^2 - 6y - 60

Step 4: Rearrange the equation:
Move all the terms to one side to form a quadratic equation:
3y^2 - 6y - 60 = 0

Step 5: Solve the quadratic equation:
To solve the quadratic equation, we can use factoring, completing the square, or the quadratic formula. If we factor the quadratic equation, we get:
(3y + 10)(y - 6) = 0

Setting each factor equal to zero, we have two possible solutions:
3y + 10 = 0 or y - 6 = 0

Solving each equation, we find:
3y = -10 or y = 6
y = -10/3

So the possible solutions for y are y = -10/3 and y = 6.