How do I factor both sides of this equation

ad-bd=bc-bd

I tried a/b =c/d that was wrong

Look at the common factors on both sides

d(a-b) = b(c-d)

What you want to do now is unclear, but go for it.

Yes Steve it's correct

So for this next equation

(a-b )d = b(c- d )
d=[ ]
can I divide both sides is this equation by a-b would it safe t0 say d=db

You divide both sides by (a-b), not by a - b

d = b(c-d)/(a-b)

To factor both sides of the equation ad - bd = bc - bd, you can follow these steps:

Step 1: Identify the common term on both sides of the equation. In this case, the common term is "-bd".

Step 2: Group the terms. On the left side of the equation, you have (ad - bd), and on the right side, you have (bc - bd). Grouping the terms helps you see the similarities and differences between the two sides.

Step 3: Factor out the common term from both groups. In this case, you can factor out "-bd" from (ad - bd) and (bc - bd), like this:

(ad - bd) = (bc - bd)
-bd(a - 1) = -bd(c - 1)

Step 4: Simplify the equation. Since both sides have "-bd", you can cancel them out:

(a - 1) = (c - 1)

Now, the equation is simplified, and you no longer have the common term "-bd" on both sides.