Solve 3(9.81)=6.67(10^-11)(m/r^2)-(w^2)r

$$3 ( 9.81 ) = 6.67 ( 10 ^ { - 11 } ) ( \frac { m } { r ^ { 2 } } ) - ( w ^ { 2 } ) r$$

Solve for m

$$m=\frac{100000000000r^{2}\left(100rw^{2}+2943\right)}{667}$$

$$r\neq 0$$

Steps for Solving Linear Equation

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

$$3\times 9.81r^{2}=6.67\times 10^{-11}m-w^{2}rr^{2}$$

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

$$3\times 9.81r^{2}=6.67\times 10^{-11}m-w^{2}r^{3}$$

Multiply 3 and 9.81 to get 29.43.

$$29.43r^{2}=6.67\times 10^{-11}m-w^{2}r^{3}$$

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$29.43r^{2}=6.67\times \frac{1}{100000000000}m-w^{2}r^{3}$$

Multiply 6.67 and \frac{1}{100000000000} to get \frac{667}{10000000000000}.

$$29.43r^{2}=\frac{667}{10000000000000}m-w^{2}r^{3}$$

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

$$\frac{667}{10000000000000}m-w^{2}r^{3}=29.43r^{2}$$

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

$$\frac{667}{10000000000000}m=29.43r^{2}+w^{2}r^{3}$$

The equation is in standard form.

$$\frac{667}{10000000000000}m=w^{2}r^{3}+\frac{2943r^{2}}{100}$$

Divide both sides of the equation by \frac{667}{10000000000000}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{667}{10000000000000}m}{\frac{667}{10000000000000}}=\frac{r^{2}\left(rw^{2}+29.43\right)}{\frac{667}{10000000000000}}$$

Dividing by \frac{667}{10000000000000} undoes the multiplication by \frac{667}{10000000000000}.

$$m=\frac{r^{2}\left(rw^{2}+29.43\right)}{\frac{667}{10000000000000}}$$

Divide r^{2}\left(29.43+w^{2}r\right) by \frac{667}{10000000000000} by multiplying r^{2}\left(29.43+w^{2}r\right) by the reciprocal of \frac{667}{10000000000000}.

$$m=\frac{10000000000000r^{2}\left(rw^{2}+29.43\right)}{667}$$