At the centre of gravity, the moment (rotational force) is 0 units.
>i.e. you could support it on a pin at that point, and it won't rotate.
the moment (in the anticlockwise direction) at the centre of gravity could be expressed as
M = 30*x - 10*(36-x)
>ignoring imperial conversion factors, because we don't particularly need them for this problem and I did my engineering degree in metric
and since we know that M is 0
0 = 30*x - 10*(36-x)
0 = 30*x - 360 + 10*x)
360 = 40*x
9 = x
The centre of gravity is 9 inches from the left.