Solve NG^-5/3-QG^1/3=KG^-5/3

$$N G ^ { - 5 / 3 } - Q G ^ { 1 / 3 } = K G ^ { - 5 / 3 }$$

Solve for K

$$K=N-QG^{2}$$

$$G\neq 0$$

Steps for Solving Linear Equation

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

$$KG^{-\frac{5}{3}}=NG^{-\frac{5}{3}}-QG^{\frac{1}{3}}$$

Reorder the terms.

$$G^{-\frac{5}{3}}K=G^{-\frac{5}{3}}N-\sqrt[3]{G}Q$$

Reorder the terms.

$$G^{-\frac{5}{3}}K=-\sqrt[3]{G}Q+G^{-\frac{5}{3}}N$$

The equation is in standard form.

$$\frac{1}{G^{\frac{5}{3}}}K=-\sqrt[3]{G}Q+\frac{N}{G^{\frac{5}{3}}}$$

Divide both sides by G^{-\frac{5}{3}}.

$$\frac{\frac{1}{G^{\frac{5}{3}}}KG^{\frac{5}{3}}}{1}=\frac{N-QG^{2}}{G^{\frac{5}{3}}\times \frac{1}{G^{\frac{5}{3}}}}$$

Dividing by G^{-\frac{5}{3}} undoes the multiplication by G^{-\frac{5}{3}}.

$$K=\frac{N-QG^{2}}{G^{\frac{5}{3}}\times \frac{1}{G^{\frac{5}{3}}}}$$

Divide \frac{-QG^{2}+N}{G^{\frac{5}{3}}} by G^{-\frac{5}{3}}.

$$K=N-QG^{2}$$

Solve for G

$$\left\{\begin{matrix}G=\sqrt{-\frac{K-N}{Q}}\text{; }G=-\sqrt{-\frac{K-N}{Q}}\text{, }&Q<0\text{ and }N<K\\G=\sqrt{\frac{N-K}{Q}}\text{; }G=-\sqrt{\frac{N-K}{Q}}\text{, }&Q>0\text{ and }N>K\\G\neq 0\text{, }&N=K\text{ and }Q=0\end{matrix}\right.$$