Solve k-fx/tx+z=d

$$\frac { k - f x } { t x + z } = d$$

Solve for d

$$d=\frac{k-fx}{tx+z}$$

$$z\neq -tx$$

Steps for Solving Linear Equation

Multiply both sides of the equation by tx+z.

$$k-fx=d\left(tx+z\right)$$

Use the distributive property to multiply d by tx+z.

$$k-fx=dtx+dz$$

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

$$dtx+dz=k-fx$$

Combine all terms containing d.

$$\left(tx+z\right)d=k-fx$$

Divide both sides by tx+z.

$$\frac{\left(tx+z\right)d}{tx+z}=\frac{k-fx}{tx+z}$$

Dividing by tx+z undoes the multiplication by tx+z.

$$d=\frac{k-fx}{tx+z}$$

Solve for f

$$\left\{\begin{matrix}f=\frac{k-dz-dtx}{x}\text{, }&z\neq -tx\text{ and }x\neq 0\\f\in \mathrm{R}\text{, }&k=dz\text{ and }x=0\text{ and }z\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by tx+z.

$$k-fx=d\left(tx+z\right)$$

Use the distributive property to multiply d by tx+z.

$$k-fx=dtx+dz$$

Subtract k from both sides.

$$-fx=dtx+dz-k$$

The equation is in standard form.

$$\left(-x\right)f=dtx+dz-k$$

Divide both sides by -x.

$$\frac{\left(-x\right)f}{-x}=\frac{dtx+dz-k}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$f=\frac{dtx+dz-k}{-x}$$

Divide dtx+dz-k by -x.

$$f=-\frac{dtx+dz-k}{x}$$