Solve k^2a-2kg-8a=0

$$k ^ { 2 } a - 2 k g - 8 a = 0$$

Solve for a

$$\left\{\begin{matrix}a=\frac{2gk}{k^{2}-8}\text{, }&|k|\neq 2\sqrt{2}\\a\in \mathrm{R}\text{, }&g=0\text{ and }|k|=2\sqrt{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2kg to both sides. Anything plus zero gives itself.

$$k^{2}a-8a=2kg$$

Combine all terms containing a.

$$\left(k^{2}-8\right)a=2kg$$

The equation is in standard form.

$$\left(k^{2}-8\right)a=2gk$$

Divide both sides by k^{2}-8.

$$\frac{\left(k^{2}-8\right)a}{k^{2}-8}=\frac{2gk}{k^{2}-8}$$

Dividing by k^{2}-8 undoes the multiplication by k^{2}-8.

$$a=\frac{2gk}{k^{2}-8}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{a\left(k^{2}-8\right)}{2k}\text{, }&k\neq 0\\g\in \mathrm{R}\text{, }&a=0\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract k^{2}a from both sides. Anything subtracted from zero gives its negation.

$$-2kg-8a=-k^{2}a$$

Add 8a to both sides.

$$-2kg=-k^{2}a+8a$$

Reorder the terms.

$$-2gk=-ak^{2}+8a$$

The equation is in standard form.

$$\left(-2k\right)g=8a-ak^{2}$$

Divide both sides by -2k.

$$\frac{\left(-2k\right)g}{-2k}=\frac{a\left(8-k^{2}\right)}{-2k}$$

Dividing by -2k undoes the multiplication by -2k.

$$g=\frac{a\left(8-k^{2}\right)}{-2k}$$

Divide a\left(-k^{2}+8\right) by -2k.

$$g=\frac{ak}{2}-\frac{4a}{k}$$