Solve Ax+bx=c

$$A x + b x = c$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=-b+\frac{c}{x}\text{, }&x\neq 0\\A\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$Ax=c-bx$$

The equation is in standard form.

$$xA=c-bx$$

Divide both sides by x.

$$\frac{xA}{x}=\frac{c-bx}{x}$$

Dividing by x undoes the multiplication by x.

$$A=\frac{c-bx}{x}$$

Divide c-bx by x.

$$A=-b+\frac{c}{x}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-A+\frac{c}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract Ax from both sides.

$$bx=c-Ax$$

The equation is in standard form.

$$xb=c-Ax$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{c-Ax}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{c-Ax}{x}$$

Divide c-Ax by x.

$$b=-A+\frac{c}{x}$$

Solve for A

$$\left\{\begin{matrix}A=-b+\frac{c}{x}\text{, }&x\neq 0\\A\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$Ax=c-bx$$

The equation is in standard form.

$$xA=c-bx$$

Divide both sides by x.

$$\frac{xA}{x}=\frac{c-bx}{x}$$

Dividing by x undoes the multiplication by x.

$$A=\frac{c-bx}{x}$$

Divide c-bx by x.

$$A=-b+\frac{c}{x}$$

Solve for b

$$\left\{\begin{matrix}b=-A+\frac{c}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract Ax from both sides.

$$bx=c-Ax$$

The equation is in standard form.

$$xb=c-Ax$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{c-Ax}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{c-Ax}{x}$$

Divide c-Ax by x.

$$b=-A+\frac{c}{x}$$