Solve ab+cd-ac-bd=a(b-c

$$a b + c d - a c - b d = a ( b - c$$

Solve for b

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

Steps for Solving Linear Equation

Use the distributive property to multiply a by b-c.

$$ab+cd-ac-bd=ab-ac$$

Subtract ab from both sides.

$$ab+cd-ac-bd-ab=-ac$$

Combine ab and -ab to get 0.

$$cd-ac-bd=-ac$$

Subtract cd from both sides.

$$-ac-bd=-ac-cd$$

Add ac to both sides.

$$-bd=-ac-cd+ac$$

Combine -ac and ac to get 0.

$$-bd=-cd$$

Cancel out -1 on both sides.

$$bd=cd$$

The equation is in standard form.

$$db=cd$$

Divide both sides by d.

$$\frac{db}{d}=\frac{cd}{d}$$

Dividing by d undoes the multiplication by d.

$$b=\frac{cd}{d}$$

Divide cd by d.

$$b=c$$

Solve for a

$$a\in \mathrm{R}$$

$$b=c\text{ or }d=0$$