Solve m*g-h_{n}(x^2)^2=m*x^0

$$m \cdot g - h _ { n } ( x ^ { 2 } ) ^ { 2 } = m \cdot x ^ { 0 }$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=\frac{h_{n}x^{4}+m}{m}\text{, }&m\neq 0\text{ and }x\neq 0\\g\in \mathrm{C}\text{, }&m=0\text{ and }h_{n}=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$mg-h_{n}x^{4}=mx^{0}$$

Add h_{n}x^{4} to both sides.

$$mg=mx^{0}+h_{n}x^{4}$$

The equation is in standard form.

$$mg=h_{n}x^{4}+m$$

Divide both sides by m.

$$\frac{mg}{m}=\frac{h_{n}x^{4}+m}{m}$$

Dividing by m undoes the multiplication by m.

$$g=\frac{h_{n}x^{4}+m}{m}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{h_{n}x^{4}+m}{m}\text{, }&m\neq 0\text{ and }x\neq 0\\g\in \mathrm{R}\text{, }&m=0\text{ and }h_{n}=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$mg-h_{n}x^{4}=mx^{0}$$

Add h_{n}x^{4} to both sides.

$$mg=mx^{0}+h_{n}x^{4}$$

The equation is in standard form.

$$mg=h_{n}x^{4}+m$$

Divide both sides by m.

$$\frac{mg}{m}=\frac{h_{n}x^{4}+m}{m}$$

Dividing by m undoes the multiplication by m.

$$g=\frac{h_{n}x^{4}+m}{m}$$

Solve for h_n

$$h_{n}=\frac{m\left(g-1\right)}{x^{4}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$mg-h_{n}x^{4}=mx^{0}$$

Subtract mg from both sides.

$$-h_{n}x^{4}=mx^{0}-mg$$

The equation is in standard form.

$$\left(-x^{4}\right)h_{n}=m-gm$$

Divide both sides by -x^{4}.

$$\frac{\left(-x^{4}\right)h_{n}}{-x^{4}}=\frac{m-gm}{-x^{4}}$$

Dividing by -x^{4} undoes the multiplication by -x^{4}.

$$h_{n}=\frac{m-gm}{-x^{4}}$$

Divide m-mg by -x^{4}.

$$h_{n}=-\frac{m\left(1-g\right)}{x^{4}}$$