Solve 6x^2y+4xy=2x^2y(3x+2)

$$6 x ^ { 2 } y + 4 x y = 2 x ^ { 2 } y ( 3 x + 2 )$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=-\frac{2}{3}\text{ or }x=1\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x^{2}y by 3x+2.

$$6x^{2}y+4xy=6x^{3}y+4x^{2}y$$

Subtract 6x^{3}y from both sides.

$$6x^{2}y+4xy-6x^{3}y=4x^{2}y$$

Subtract 4x^{2}y from both sides.

$$6x^{2}y+4xy-6x^{3}y-4x^{2}y=0$$

Combine 6x^{2}y and -4x^{2}y to get 2x^{2}y.

$$2x^{2}y+4xy-6x^{3}y=0$$

Combine all terms containing y.

$$\left(2x^{2}+4x-6x^{3}\right)y=0$$

The equation is in standard form.

$$\left(4x+2x^{2}-6x^{3}\right)y=0$$

Divide 0 by 2x^{2}+4x-6x^{3}.

$$y=0$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=-\frac{2}{3}\text{ or }x=1\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x^{2}y by 3x+2.

$$6x^{2}y+4xy=6x^{3}y+4x^{2}y$$

Subtract 6x^{3}y from both sides.

$$6x^{2}y+4xy-6x^{3}y=4x^{2}y$$

Subtract 4x^{2}y from both sides.

$$6x^{2}y+4xy-6x^{3}y-4x^{2}y=0$$

Combine 6x^{2}y and -4x^{2}y to get 2x^{2}y.

$$2x^{2}y+4xy-6x^{3}y=0$$

Combine all terms containing y.

$$\left(2x^{2}+4x-6x^{3}\right)y=0$$

The equation is in standard form.

$$\left(4x+2x^{2}-6x^{3}\right)y=0$$

Divide 0 by 2x^{2}+4x-6x^{3}.

$$y=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=1\text{; }x=0\text{; }x=-\frac{2}{3}\approx -0.666666667\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=1\text{; }x=0\text{; }x=-\frac{2}{3}\approx -0.666666667\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$