Solve S_{6}*S_{12}=2kg*x

$$S _ { 6 } \cdot S _ { 12 } = 2 kg \cdot x$$

Solve for S_12 (complex solution)

$$\left\{\begin{matrix}S_{12}=\frac{2gkx}{S_{6}}\text{, }&S_{6}\neq 0\\S_{12}\in \mathrm{C}\text{, }&\left(k=0\text{ or }g=0\text{ or }x=0\right)\text{ and }S_{6}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$S_{6}S_{12}=2gkx$$

Divide both sides by S_{6}.

$$\frac{S_{6}S_{12}}{S_{6}}=\frac{2gkx}{S_{6}}$$

Dividing by S_{6} undoes the multiplication by S_{6}.

$$S_{12}=\frac{2gkx}{S_{6}}$$

Solve for S_6 (complex solution)

$$\left\{\begin{matrix}S_{6}=\frac{2gkx}{S_{12}}\text{, }&S_{12}\neq 0\\S_{6}\in \mathrm{C}\text{, }&\left(k=0\text{ or }g=0\text{ or }x=0\right)\text{ and }S_{12}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$S_{12}S_{6}=2gkx$$

Divide both sides by S_{12}.

$$\frac{S_{12}S_{6}}{S_{12}}=\frac{2gkx}{S_{12}}$$

Dividing by S_{12} undoes the multiplication by S_{12}.

$$S_{6}=\frac{2gkx}{S_{12}}$$

Solve for S_12

$$\left\{\begin{matrix}S_{12}=\frac{2gkx}{S_{6}}\text{, }&S_{6}\neq 0\\S_{12}\in \mathrm{R}\text{, }&\left(k=0\text{ or }g=0\text{ or }x=0\right)\text{ and }S_{6}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$S_{6}S_{12}=2gkx$$

Divide both sides by S_{6}.

$$\frac{S_{6}S_{12}}{S_{6}}=\frac{2gkx}{S_{6}}$$

Dividing by S_{6} undoes the multiplication by S_{6}.

$$S_{12}=\frac{2gkx}{S_{6}}$$

Solve for S_6

$$\left\{\begin{matrix}S_{6}=\frac{2gkx}{S_{12}}\text{, }&S_{12}\neq 0\\S_{6}\in \mathrm{R}\text{, }&\left(k=0\text{ or }g=0\text{ or }x=0\right)\text{ and }S_{12}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$S_{12}S_{6}=2gkx$$

Divide both sides by S_{12}.

$$\frac{S_{12}S_{6}}{S_{12}}=\frac{2gkx}{S_{12}}$$

Dividing by S_{12} undoes the multiplication by S_{12}.

$$S_{6}=\frac{2gkx}{S_{12}}$$