Solve y=3xdx

$$y = 3 x d x$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$y=3x^{2}d$$

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

$$3x^{2}d=y$$

Divide both sides by 3x^{2}.

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

Dividing by 3x^{2} undoes the multiplication by 3x^{2}.

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

Solve for d

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

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$y=3x^{2}d$$

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

$$3x^{2}d=y$$

Divide both sides by 3x^{2}.

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

Dividing by 3x^{2} undoes the multiplication by 3x^{2}.

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{d^{-\frac{1}{2}}\sqrt{3y}}{3}\text{; }x=\frac{d^{-\frac{1}{2}}\sqrt{3y}}{3}\text{, }&d\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }d=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{\frac{3y}{d}}}{3}\text{; }x=-\frac{\sqrt{\frac{3y}{d}}}{3}\text{, }&\left(y\geq 0\text{ and }d>0\right)\text{ or }\left(y\leq 0\text{ and }d<0\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }d=0\end{matrix}\right.$$