Solve L=-3kx+3/2kx^2

$$L = - 3 k x + \frac { 3 } { 2 } k x ^ { 2 }$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{2L}{3x\left(x-2\right)}\text{, }&x\neq 2\text{ and }x\neq 0\\k\in \mathrm{C}\text{, }&\left(x=0\text{ or }x=2\right)\text{ and }L=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-3kx+\frac{3}{2}kx^{2}=L$$

Combine all terms containing k.

$$\left(-3x+\frac{3}{2}x^{2}\right)k=L$$

The equation is in standard form.

$$\left(\frac{3x^{2}}{2}-3x\right)k=L$$

Divide both sides by -3x+\frac{3}{2}x^{2}.

$$\frac{\left(\frac{3x^{2}}{2}-3x\right)k}{\frac{3x^{2}}{2}-3x}=\frac{L}{\frac{3x^{2}}{2}-3x}$$

Dividing by -3x+\frac{3}{2}x^{2} undoes the multiplication by -3x+\frac{3}{2}x^{2}.

$$k=\frac{L}{\frac{3x^{2}}{2}-3x}$$

Divide L by -3x+\frac{3}{2}x^{2}.

$$k=\frac{2L}{3x\left(x-2\right)}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{2L}{3x\left(x-2\right)}\text{, }&x\neq 2\text{ and }x\neq 0\\k\in \mathrm{R}\text{, }&\left(x=0\text{ or }x=2\right)\text{ and }L=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-3kx+\frac{3}{2}kx^{2}=L$$

Combine all terms containing k.

$$\left(-3x+\frac{3}{2}x^{2}\right)k=L$$

The equation is in standard form.

$$\left(\frac{3x^{2}}{2}-3x\right)k=L$$

Divide both sides by -3x+\frac{3}{2}x^{2}.

$$\frac{\left(\frac{3x^{2}}{2}-3x\right)k}{\frac{3x^{2}}{2}-3x}=\frac{L}{\frac{3x^{2}}{2}-3x}$$

Dividing by -3x+\frac{3}{2}x^{2} undoes the multiplication by -3x+\frac{3}{2}x^{2}.

$$k=\frac{L}{\frac{3x^{2}}{2}-3x}$$

Divide L by -3x+\frac{3}{2}x^{2}.

$$k=\frac{2L}{3x\left(x-2\right)}$$

Solve for L

$$L=\frac{3kx\left(x-2\right)}{2}$$