Solve Ax-b=Cx+d

$$A x - b = C x + d$$

Solve for A

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

Steps for Solving Linear Equation

Add b to both sides.

$$Ax=Cx+d+b$$

The equation is in standard form.

$$xA=Cx+b+d$$

Divide both sides by x.

$$\frac{xA}{x}=\frac{Cx+b+d}{x}$$

Dividing by x undoes the multiplication by x.

$$A=\frac{Cx+b+d}{x}$$

Solve for C

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

Steps for Solving Linear Equation

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

$$Cx+d=Ax-b$$

Subtract d from both sides.

$$Cx=Ax-b-d$$

The equation is in standard form.

$$xC=Ax-b-d$$

Divide both sides by x.

$$\frac{xC}{x}=\frac{Ax-b-d}{x}$$

Dividing by x undoes the multiplication by x.

$$C=\frac{Ax-b-d}{x}$$