Solve y=3Lk^2

$$y = 3 L k ^ { 2 }$$

Solve for L (complex solution)

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

Steps for Solving Linear Equation

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

$$3Lk^{2}=y$$

The equation is in standard form.

$$3k^{2}L=y$$

Divide both sides by 3k^{2}.

$$\frac{3k^{2}L}{3k^{2}}=\frac{y}{3k^{2}}$$

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

$$L=\frac{y}{3k^{2}}$$

Solve for L

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

Steps for Solving Linear Equation

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

$$3Lk^{2}=y$$

The equation is in standard form.

$$3k^{2}L=y$$

Divide both sides by 3k^{2}.

$$\frac{3k^{2}L}{3k^{2}}=\frac{y}{3k^{2}}$$

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

$$L=\frac{y}{3k^{2}}$$

Solve for k (complex solution)

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

Solve for k

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