Solve for g f=2gh+2gk

$f = 2 g h + 2 g k$

Step 1

Rewrite the equation as $2 g h + 2 g k = f$ .

$2 g h + 2 g k = f$

Step 2

Factor $2 g$ out of $2 g h + 2 g k$ .

Factor $2 g$ out of $2 g h$ .

$2 g (h) + 2 g k = f$

Factor $2 g$ out of $2 g k$ .

$2 g (h) + 2 g (k) = f$

Factor $2 g$ out of $2 g (h) + 2 g (k)$ .

$2 g (h + k) = f$

Step 3

Divide each term in $2 g (h + k) = f$ by $2 (h + k)$ and simplify.

Divide each term in $2 g (h + k) = f$ by $2 (h + k)$ .

$\frac{2 g (h + k)}{2 (h + k)} = \frac{f}{2 (h + k)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 g (h + k)}{2 (h + k)} = \frac{f}{2 (h + k)}$

Rewrite the expression.

$\frac{g (h + k)}{h + k} = \frac{f}{2 (h + k)}$

Cancel the common factor of $h + k$ .

Cancel the common factor.

$\frac{g (h + k)}{h + k} = \frac{f}{2 (h + k)}$

Divide $g$ by $1$ .

$g = \frac{f}{2 (h + k)}$