Solve for f 6f+9g=3g+f

$6 f + 9 g = 3 g + f$

Move all terms containing $f$ to the left side of the equation.

Subtract $f$ from both sides of the equation.

$6 f + 9 g - f = 3 g$

Subtract $f$ from $6 f$ .

$5 f + 9 g = 3 g$

Move all terms not containing $f$ to the right side of the equation.

Subtract $9 g$ from both sides of the equation.

$5 f = 3 g - 9 g$

Subtract $9 g$ from $3 g$ .

$5 f = - 6 g$

Divide each term in $5 f = - 6 g$ by $5$ and simplify.

Divide each term in $5 f = - 6 g$ by $5$ .

$\frac{5 f}{5} = \frac{- 6 g}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 f}{5} = \frac{- 6 g}{5}$

Divide $f$ by $1$ .

$f = \frac{- 6 g}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$f = - \frac{6 g}{5}$