Solve 3g=ym/r^2-w^2r

$$3g = y \frac{ m }{ { r }^{ 2 } } - { w }^{ 2 } r$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{r^{2}\left(rw^{2}+3g\right)}{y}\text{, }&y\neq 0\text{ and }r\neq 0\\m\in \mathrm{C}\text{, }&g=-\frac{rw^{2}}{3}\text{ and }y=0\text{ and }r\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r^{2}.

$$3gr^{2}=ym-w^{2}rr^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3gr^{2}=ym-w^{2}r^{3}$$

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

$$ym-w^{2}r^{3}=3gr^{2}$$

Add w^{2}r^{3} to both sides.

$$ym=3gr^{2}+w^{2}r^{3}$$

Divide both sides by y.

$$\frac{ym}{y}=\frac{r^{2}\left(rw^{2}+3g\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$m=\frac{r^{2}\left(rw^{2}+3g\right)}{y}$$

Solve for g

$$g=-\frac{rw^{2}}{3}+\frac{my}{3r^{2}}$$

$$r\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r^{2}.

$$3gr^{2}=ym-w^{2}rr^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3gr^{2}=ym-w^{2}r^{3}$$

Reorder the terms.

$$3gr^{2}=my-w^{2}r^{3}$$

The equation is in standard form.

$$3r^{2}g=my-w^{2}r^{3}$$

Divide both sides by 3r^{2}.

$$\frac{3r^{2}g}{3r^{2}}=\frac{my-w^{2}r^{3}}{3r^{2}}$$

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

$$g=\frac{my-w^{2}r^{3}}{3r^{2}}$$

Divide my-w^{2}r^{3} by 3r^{2}.

$$g=-\frac{rw^{2}}{3}+\frac{my}{3r^{2}}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{r^{2}\left(rw^{2}+3g\right)}{y}\text{, }&y\neq 0\text{ and }r\neq 0\\m\in \mathrm{R}\text{, }&g=-\frac{rw^{2}}{3}\text{ and }y=0\text{ and }r\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r^{2}.

$$3gr^{2}=ym-w^{2}rr^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3gr^{2}=ym-w^{2}r^{3}$$

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

$$ym-w^{2}r^{3}=3gr^{2}$$

Add w^{2}r^{3} to both sides.

$$ym=3gr^{2}+w^{2}r^{3}$$

Divide both sides by y.

$$\frac{ym}{y}=\frac{r^{2}\left(rw^{2}+3g\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$m=\frac{r^{2}\left(rw^{2}+3g\right)}{y}$$