Solve x=2xy+3x

$$x=2xy+3x$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Subtract 2xy from both sides.

$$x-2xy=3x$$

Subtract 3x from both sides.

$$x-2xy-3x=0$$

Combine x and -3x to get -2x.

$$-2x-2xy=0$$

Combine all terms containing x.

$$\left(-2-2y\right)x=0$$

The equation is in standard form.

$$\left(-2y-2\right)x=0$$

Divide 0 by -2-2y.

$$x=0$$

Solve for y (complex solution)

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2xy+3x=x$$

Subtract 3x from both sides.

$$2xy=x-3x$$

Combine x and -3x to get -2x.

$$2xy=-2x$$

Divide both sides by 2x.

$$\frac{2xy}{2x}=-\frac{2x}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$y=-\frac{2x}{2x}$$

Divide -2x by 2x.

$$y=-1$$

Solve for x

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

Steps for Solving Linear Equation

Subtract 2xy from both sides.

$$x-2xy=3x$$

Subtract 3x from both sides.

$$x-2xy-3x=0$$

Combine x and -3x to get -2x.

$$-2x-2xy=0$$

Combine all terms containing x.

$$\left(-2-2y\right)x=0$$

The equation is in standard form.

$$\left(-2y-2\right)x=0$$

Divide 0 by -2-2y.

$$x=0$$

Solve for y

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2xy+3x=x$$

Subtract 3x from both sides.

$$2xy=x-3x$$

Combine x and -3x to get -2x.

$$2xy=-2x$$

Divide both sides by 2x.

$$\frac{2xy}{2x}=-\frac{2x}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$y=-\frac{2x}{2x}$$

Divide -2x by 2x.

$$y=-1$$