Solve 375J=1/2(12ky)v^2

$$375 J = 1 / 2 ( 12 k y ) v ^ { 2 }$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{125J}{2yv^{2}}\text{, }&v\neq 0\text{ and }y\neq 0\\k\in \mathrm{C}\text{, }&\left(y=0\text{ or }v=0\right)\text{ and }J=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply \frac{1}{2} and 12 to get 6.

$$375J=6kyv^{2}$$

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

$$6kyv^{2}=375J$$

The equation is in standard form.

$$6yv^{2}k=375J$$

Divide both sides by 6yv^{2}.

$$\frac{6yv^{2}k}{6yv^{2}}=\frac{375J}{6yv^{2}}$$

Dividing by 6yv^{2} undoes the multiplication by 6yv^{2}.

$$k=\frac{375J}{6yv^{2}}$$

Divide 375J by 6yv^{2}.

$$k=\frac{125J}{2yv^{2}}$$

Solve for J

$$J=\frac{2kyv^{2}}{125}$$

Steps for Solving Linear Equation

Multiply \frac{1}{2} and 12 to get 6.

$$375J=6kyv^{2}$$

Divide both sides by 375.

$$\frac{375J}{375}=\frac{6kyv^{2}}{375}$$

Dividing by 375 undoes the multiplication by 375.

$$J=\frac{6kyv^{2}}{375}$$

Divide 6kyv^{2} by 375.

$$J=\frac{2kyv^{2}}{125}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{125J}{2yv^{2}}\text{, }&v\neq 0\text{ and }y\neq 0\\k\in \mathrm{R}\text{, }&\left(y=0\text{ or }v=0\right)\text{ and }J=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply \frac{1}{2} and 12 to get 6.

$$375J=6kyv^{2}$$

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

$$6kyv^{2}=375J$$

The equation is in standard form.

$$6yv^{2}k=375J$$

Divide both sides by 6yv^{2}.

$$\frac{6yv^{2}k}{6yv^{2}}=\frac{375J}{6yv^{2}}$$

Dividing by 6yv^{2} undoes the multiplication by 6yv^{2}.

$$k=\frac{375J}{6yv^{2}}$$

Divide 375J by 6yv^{2}.

$$k=\frac{125J}{2yv^{2}}$$