Capacitor is charged then connected to a capacitor and battery

Hello PF,

1. The problem statement, all variables and given/known data
The capacitor C_1 is connected to a battery as shown. After being charged, it is connected to the capacitor C_2 and the second battery as shown. When all the charges come to rest, what will be the charge on capacitor C_2?

2. Relevant equations
C = Q/V

3. The attempt at a solution
The initial charge on C_1 is Q_1 = C_1 V_1
After it is connected to the other circuit and in steady state, I used the loop rule to get the equation (q_1/C_1) + (q_2/C_2) = V_2, where q_1 is the new charge on C_1 and q_2 is the charge on C_2.
Now the problem is relating q_1, q_2 and Q_1. According to my professor’s solution, -Q_1 = -q_1 + q_2.
He got that equation by doing what’s shown here:, and I have no idea where he got that from, and this is the point that I’m stuck on and why I’m posting this.
Using that equation we can find q_2 easily, but I don’t understand how he got it.

Thank you.

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