Solve for y ky-bf=(fy)/m

$k y - b f = \frac{f y}{m}$

Step 1

Multiply both sides by $m$ .

$(k y - b f) m = \frac{f y}{m} m$

Step 2

Simplify.

Simplify the left side.

Simplify $(k y - b f) m$ .

Apply the distributive property.

$k y m - b f m = \frac{f y}{m} m$

Simplify the expression.

Move $y$ .

$k m y - b f m = \frac{f y}{m} m$

Reorder $k m y$ and $- b f m$ .

$- b f m + k m y = \frac{f y}{m} m$

Simplify the right side.

Cancel the common factor of $m$ .

Cancel the common factor.

$- b f m + k m y = \frac{f y}{m} m$

Rewrite the expression.

$- b f m + k m y = f y$

Step 3

Solve for $y$ .

Subtract $f y$ from both sides of the equation.

$- b f m + k m y - f y = 0$

Add $b f m$ to both sides of the equation.

$k m y - f y = b f m$

Factor $y$ out of $k m y - f y$ .

Factor $y$ out of $k m y$ .

$y (k m) - f y = b f m$

Factor $y$ out of $- f y$ .

$y (k m) + y (- f) = b f m$

Factor $y$ out of $y (k m) + y (- f)$ .

$y (k m - f) = b f m$

Divide each term in $y (k m - f) = b f m$ by $k m - f$ and simplify.

Divide each term in $y (k m - f) = b f m$ by $k m - f$ .

$\frac{y (k m - f)}{k m - f} = \frac{b f m}{k m - f}$

Simplify the left side.

Cancel the common factor of $k m - f$ .

Cancel the common factor.

$\frac{y (k m - f)}{k m - f} = \frac{b f m}{k m - f}$

Divide $y$ by $1$ .

$y = \frac{b f m}{k m - f}$