Energy conservation of a child on a swing

[mikefitz]

The maximum speed of a child on a swing is 4.9 m/s. The child’s height above the ground at the lowest point is 0.7 m. How high above the ground is he at his highest point?
http://img208.imageshack.us/img208/9949/untitledyx0.png

Above is the work done to solve the problem. I don't understand how they went from the blue to the red equation. Wouldn't the two g's cancel out since you would need to divide the left side by mg?

 

[Doc Al]

Wouldn't the two g's cancel out since you would need to divide the left side by mg?

You divide all terms by mg. The m's all cancel, since an m appears in all three terms. But g's only cancel in the two terms that had g's--the KE term does not have a g to cancel.