Solve 37.5J=1/2(12ky)v^2

$$37.5 J = 1 / 2 ( 12 k y ) v ^ { 2 }$$

Solve for J

$$J=\frac{4kyv^{2}}{25}$$

Steps for Solving Linear Equation

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

$$37.5J=6kyv^{2}$$

Divide both sides of the equation by 37.5, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{37.5J}{37.5}=\frac{6kyv^{2}}{37.5}$$

Dividing by 37.5 undoes the multiplication by 37.5.

$$J=\frac{6kyv^{2}}{37.5}$$

Divide 6kyv^{2} by 37.5 by multiplying 6kyv^{2} by the reciprocal of 37.5.

$$J=\frac{4kyv^{2}}{25}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{25J}{4yv^{2}}\text{, }&v\neq 0\text{ and }y\neq 0\\k\in \mathrm{R}\text{, }&\left(y=0\text{ or }v=0\right)\text{ and }J=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$37.5J=6kyv^{2}$$

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

$$6kyv^{2}=37.5J$$

The equation is in standard form.

$$6yv^{2}k=\frac{75J}{2}$$

Divide both sides by 6yv^{2}.

$$\frac{6yv^{2}k}{6yv^{2}}=\frac{75J}{2\times 6yv^{2}}$$

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

$$k=\frac{75J}{2\times 6yv^{2}}$$

Divide \frac{75J}{2} by 6yv^{2}.

$$k=\frac{25J}{4yv^{2}}$$