Most likely the rules for manipulating equations will be found in any decent Algebra 1 text.

I suspect that your problem is not so much with the rules themselves, but with the arithmetic or algebraic operations involved. Why? Because the rules themselves are indeed trivial. Moreover, there are just so many of them. Let A, B, C, ... stand for some mathematical expressions that may or may not include variables. Then

1. If A = B
and C = D,
then A+C = B+D, A-C = B-D, A*C = B*D, A/C = B/D.

(The latter only applicable where neither C, nor D is 0.)

2. If A = B
and c is not 0,
then cA = cB and c + A = c + B.

(This is a particular case of 1, where C = D = c.)

3. If A = B,
and a > 0,
then a^A = a^B

#2 and #3 examplify that dictum "Whatever you do to the left side do to the right side as well.

All the best,
Alexander Bogomolny