Solve P^2=4pi^2/GMa^3

$$P ^ { 2 } = \frac { 4 \pi ^ { 2 } } { G M } a ^ { 3 }$$

Solve for G

$$\left\{\begin{matrix}G=\frac{4\times \left(\frac{\pi }{P}\right)^{2}a^{3}}{M}\text{, }&a\neq 0\text{ and }M\neq 0\text{ and }P\neq 0\\G\neq 0\text{, }&P=0\text{ and }a=0\text{ and }M\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable G cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by GM.

$$GMP^{2}=4\pi ^{2}a^{3}$$

The equation is in standard form.

$$MP^{2}G=4\pi ^{2}a^{3}$$

Divide both sides by MP^{2}.

$$\frac{MP^{2}G}{MP^{2}}=\frac{4\pi ^{2}a^{3}}{MP^{2}}$$

Dividing by MP^{2} undoes the multiplication by MP^{2}.

$$G=\frac{4\pi ^{2}a^{3}}{MP^{2}}$$

Variable G cannot be equal to 0.

$$G=\frac{4\pi ^{2}a^{3}}{MP^{2}}\text{, }G\neq 0$$

Solve for M

$$\left\{\begin{matrix}M=\frac{4\times \left(\frac{\pi }{P}\right)^{2}a^{3}}{G}\text{, }&a\neq 0\text{ and }G\neq 0\text{ and }P\neq 0\\M\neq 0\text{, }&P=0\text{ and }a=0\text{ and }G\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable M cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by GM.

$$GMP^{2}=4\pi ^{2}a^{3}$$

The equation is in standard form.

$$GP^{2}M=4\pi ^{2}a^{3}$$

Divide both sides by GP^{2}.

$$\frac{GP^{2}M}{GP^{2}}=\frac{4\pi ^{2}a^{3}}{GP^{2}}$$

Dividing by GP^{2} undoes the multiplication by GP^{2}.

$$M=\frac{4\pi ^{2}a^{3}}{GP^{2}}$$

Variable M cannot be equal to 0.

$$M=\frac{4\pi ^{2}a^{3}}{GP^{2}}\text{, }M\neq 0$$