Solve for K F=2KG+2KH

$F = 2 K G + 2 K H$

Rewrite the equation as $2 K G + 2 K H = F$ .

$2 K G + 2 K H = F$

Factor $2 K$ out of $2 K G + 2 K H$ .

Factor $2 K$ out of $2 K G$ .

$2 K (G) + 2 K H = F$

Factor $2 K$ out of $2 K H$ .

$2 K (G) + 2 K (H) = F$

Factor $2 K$ out of $2 K (G) + 2 K (H)$ .

$2 K (G + H) = F$

Divide each term in $2 K (G + H) = F$ by $2 (G + H)$ and simplify.

Divide each term in $2 K (G + H) = F$ by $2 (G + H)$ .

$\frac{2 K (G + H)}{2 (G + H)} = \frac{F}{2 (G + H)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 K (G + H)}{2 (G + H)} = \frac{F}{2 (G + H)}$

Rewrite the expression.

$\frac{K (G + H)}{G + H} = \frac{F}{2 (G + H)}$

Cancel the common factor of $G + H$ .

Cancel the common factor.

$\frac{K (G + H)}{G + H} = \frac{F}{2 (G + H)}$

Divide $K$ by $1$ .

$K = \frac{F}{2 (G + H)}$