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

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

Solve for g

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

$$r\neq 0$$

Steps for Solving Linear Equation

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

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

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

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

The equation is in standard form.

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

Divide both sides by 3r^{2}.

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

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

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

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

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

Solve for m

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

$$r\neq 0$$