Solve 3m+40cm=xdm

$$3 m + 40 c m = x d m$$

Solve for c (complex solution)

$$\left\{\begin{matrix}\\c=\frac{dx-3}{40}\text{, }&\text{unconditionally}\\c\in \mathrm{C}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3m from both sides.

$$40cm=xdm-3m$$

The equation is in standard form.

$$40mc=dmx-3m$$

Divide both sides by 40m.

$$\frac{40mc}{40m}=\frac{m\left(dx-3\right)}{40m}$$

Dividing by 40m undoes the multiplication by 40m.

$$c=\frac{m\left(dx-3\right)}{40m}$$

Divide m\left(xd-3\right) by 40m.

$$c=\frac{dx-3}{40}$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{40c+3}{x}\text{, }&x\neq 0\\d\in \mathrm{C}\text{, }&m=0\text{ or }\left(c=-\frac{3}{40}\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$xdm=3m+40cm$$

The equation is in standard form.

$$mxd=40cm+3m$$

Divide both sides by xm.

$$\frac{mxd}{mx}=\frac{m\left(40c+3\right)}{mx}$$

Dividing by xm undoes the multiplication by xm.

$$d=\frac{m\left(40c+3\right)}{mx}$$

Divide m\left(3+40c\right) by xm.

$$d=\frac{40c+3}{x}$$

Solve for c

$$\left\{\begin{matrix}\\c=\frac{dx-3}{40}\text{, }&\text{unconditionally}\\c\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3m from both sides.

$$40cm=xdm-3m$$

The equation is in standard form.

$$40mc=dmx-3m$$

Divide both sides by 40m.

$$\frac{40mc}{40m}=\frac{m\left(dx-3\right)}{40m}$$

Dividing by 40m undoes the multiplication by 40m.

$$c=\frac{m\left(dx-3\right)}{40m}$$

Divide m\left(xd-3\right) by 40m.

$$c=\frac{dx-3}{40}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{40c+3}{x}\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&m=0\text{ or }\left(c=-\frac{3}{40}\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$xdm=3m+40cm$$

The equation is in standard form.

$$mxd=40cm+3m$$

Divide both sides by xm.

$$\frac{mxd}{mx}=\frac{m\left(40c+3\right)}{mx}$$

Dividing by xm undoes the multiplication by xm.

$$d=\frac{m\left(40c+3\right)}{mx}$$

Divide m\left(3+40c\right) by xm.

$$d=\frac{40c+3}{x}$$