Solve 3y/2x^2=2y

$$\frac { 3 y } { 2 x ^ { 2 } } = 2 y$$

Solve for y (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x^{2}.

$$3y=2y\times 2x^{2}$$

Multiply 2 and 2 to get 4.

$$3y=4yx^{2}$$

Subtract 4yx^{2} from both sides.

$$3y-4yx^{2}=0$$

Combine all terms containing y.

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

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

$$y=0$$

Solve for y

$$\left\{\begin{matrix}y=0\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&|x|=\frac{\sqrt{3}}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x^{2}.

$$3y=2y\times 2x^{2}$$

Multiply 2 and 2 to get 4.

$$3y=4yx^{2}$$

Subtract 4yx^{2} from both sides.

$$3y-4yx^{2}=0$$

Combine all terms containing y.

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

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

$$y=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-\frac{\sqrt{3}}{2}\approx -0.866025404\text{; }x=\frac{\sqrt{3}}{2}\approx 0.866025404\text{, }&\text{unconditionally}\\x\neq 0\text{, }&y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{\sqrt{3}}{2}\approx 0.866025404\text{; }x=-\frac{\sqrt{3}}{2}\approx -0.866025404\text{, }&\text{unconditionally}\\x\neq 0\text{, }&y=0\end{matrix}\right.$$