Solve ax+bx=cx

$$a x + b x = c x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=c-b\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$ax=cx-bx$$

The equation is in standard form.

$$xa=cx-bx$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{x\left(c-b\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{x\left(c-b\right)}{x}$$

Divide x\left(c-b\right) by x.

$$a=c-b$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=c-a\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ax from both sides.

$$bx=cx-ax$$

The equation is in standard form.

$$xb=cx-ax$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{x\left(c-a\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{x\left(c-a\right)}{x}$$

Divide x\left(c-a\right) by x.

$$b=c-a$$

Solve for a

$$\left\{\begin{matrix}\\a=c-b\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$ax=cx-bx$$

The equation is in standard form.

$$xa=cx-bx$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{x\left(c-b\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{x\left(c-b\right)}{x}$$

Divide x\left(c-b\right) by x.

$$a=c-b$$

Solve for b

$$\left\{\begin{matrix}\\b=c-a\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ax from both sides.

$$bx=cx-ax$$

The equation is in standard form.

$$xb=cx-ax$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{x\left(c-a\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{x\left(c-a\right)}{x}$$

Divide x\left(c-a\right) by x.

$$b=c-a$$