\( 3 y+5 x(2-4 y)=6-2 y \) for \( y \)

To solve the equation \( 3y + 5x(2 - 4y) = 6 - 2y \) for \( y \), we can start by expanding it and then isolating \( y \). First, expand the equation: \[ 3y + 10x - 20xy = 6 - 2y \] Now, let's group all the \( y \) terms on one side: \[ 3y + 2y + 20xy = 6 - 10x \] This simplifies to: \[ (3 + 20x + 2)y = 6 - 10x \] Now, factor out \( y \): \[ y(20x + 5) = 6 - 10x \] Next, isolate \( y \): \[ y = \frac{6 - 10x}{20x + 5} \] And that's your solution for \( y \): \[ y = \frac{6 - 10x}{20x + 5} \] Feel free to substitute values for \( x \) to see how \( y \) behaves!