I'm going through the following heat equation problem, and I understand how the solution is constructed except for one algebraic re-arrangement that I can't make sense of (and its probably really obvious) which is right at the start of the solution. I was hoping someone could enlighten me.

Solve on with IC's and BC's .

The example says:

Let .

Confused from here:

Sub in

Then .

To the line above

From here I have no problems understanding and solving this problem.

This is probably embarrassingly simple, but I keep getting

and why is this equal to (Thinking)