Solve H_{2}+F_{2}=2HF

$$H _ { 2 } + F _ { 2 } = 2 HF$$

Solve for F

$$\left\{\begin{matrix}F=\frac{F_{2}+H_{2}}{2H}\text{, }&H\neq 0\\F\in \mathrm{R}\text{, }&H_{2}=-F_{2}\text{ and }H=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2HF=H_{2}+F_{2}$$

The equation is in standard form.

$$2HF=F_{2}+H_{2}$$

Divide both sides by 2H.

$$\frac{2HF}{2H}=\frac{F_{2}+H_{2}}{2H}$$

Dividing by 2H undoes the multiplication by 2H.

$$F=\frac{F_{2}+H_{2}}{2H}$$

Solve for F_2

$$F_{2}=-\left(H_{2}-2FH\right)$$

Solution Steps

Subtract H_{2} from both sides.

$$F_{2}=2HF-H_{2}$$