Solve 6x^2-4x^3y=24x^3y

$$6 x ^ { 2 } - 4 x ^ { 3 } y = 24 x ^ { 3 } y$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{3}{14x}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 24x^{3}y from both sides.

$$6x^{2}-4x^{3}y-24x^{3}y=0$$

Combine -4x^{3}y and -24x^{3}y to get -28x^{3}y.

$$6x^{2}-28x^{3}y=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-28x^{3}y=-6x^{2}$$

The equation is in standard form.

$$\left(-28x^{3}\right)y=-6x^{2}$$

Divide both sides by -28x^{3}.

$$\frac{\left(-28x^{3}\right)y}{-28x^{3}}=-\frac{6x^{2}}{-28x^{3}}$$

Dividing by -28x^{3} undoes the multiplication by -28x^{3}.

$$y=-\frac{6x^{2}}{-28x^{3}}$$

Divide -6x^{2} by -28x^{3}.

$$y=\frac{3}{14x}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{3}{14x}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 24x^{3}y from both sides.

$$6x^{2}-4x^{3}y-24x^{3}y=0$$

Combine -4x^{3}y and -24x^{3}y to get -28x^{3}y.

$$6x^{2}-28x^{3}y=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-28x^{3}y=-6x^{2}$$

The equation is in standard form.

$$\left(-28x^{3}\right)y=-6x^{2}$$

Divide both sides by -28x^{3}.

$$\frac{\left(-28x^{3}\right)y}{-28x^{3}}=-\frac{6x^{2}}{-28x^{3}}$$

Dividing by -28x^{3} undoes the multiplication by -28x^{3}.

$$y=-\frac{6x^{2}}{-28x^{3}}$$

Divide -6x^{2} by -28x^{3}.

$$y=\frac{3}{14x}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{3}{14y}\text{, }&y\neq 0\end{matrix}\right.$$