(2y+x)-3xy = 0

To solve the equation \( (2y + x) - 3xy = 0 \), we can start by rearranging it:

\[
2y + x - 3xy = 0
\]

Rearranging gives:

\[
2y + x = 3xy
\]

Now, let's isolate one of the variables; we can express \( y \) in terms of \( x \):

\[
2y = 3xy - x
\]

Factoring out \( x \) from the right side:

\[
2y = x(3y - 1)
\]

Now, if we divide both sides by \( 2 \):

\[
y = \frac{x(3y - 1)}{2}
\]

To isolate \( y \), we can multiply both sides by \( 2 \):

\[
2y = x(3y - 1)
\]

Expanding the right side, we get:

\[
2y = 3xy - x
\]

Now, rearranging this gives:

\[
2y - 3xy + x = 0
\]

This is a linear equation in \( y \). To solve for \( y \) explicitly, we can arrange it as:

\[
y(2 - 3x) = -x
\]

Then we can solve for \( y \):

\[
y = \frac{-x}{2 - 3x}
\]

Thus, the solution to the equation \( (2y + x) - 3xy = 0 \) is:

\[
y = \frac{-x}{2 - 3x}
\]

Please let me know if you need further assistance or any more detail on the topic!