Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

I drive at an average speed of 30 miles per hour to the railroad station each morning and catch my train. On a particular morning, there was a lot of traffic and at the halfway point, I had averaged only 15 miles per hour. How fast must I drive for the rest of the way to catch my train?

Take away the whole and some still remain. What is it?

A red house is made out of red bricks. A yellow house is made out of yellow bricks. And, a blue house is made out of blue bricks. So, what is a greenhouse made of?

You have a 12 liters jug full of water. You have two empty 8 liters and 5 liters jug. How can you divide the water into two equal parts using these jugs?

The horse jumps over the king.
Strangely there is absolutely no scratch on him.

Can anyone explain, how is this possible?

John was gifted a new Hayabusa. He drove x miles at 55mph. Then he drove x+20 miles at 40mps. He drove his bike for 100 minutes. How much distance did he travel?

In a mathematical quiz, you are asked the following question:

Use three 9s in a mathematical expression without dividing or multiplying to form the number one.

Can you answer the question?

You need to arrange three 7 and mathematical symbols to form number 1?

There's one "sport" in which neither the spectators nor the participants know the score or the leader until the contest ends.

What is it?