Final answer:
The question seems to contain a mix of unrelated mathematical and physics equations, but the initial prompt 'Find the quotient' suggests a division problem. An exact answer can't be given without further clarification, but typically this involves dividing a number by 12 and finding the remainder.
Step-by-step explanation:
The provided details are confusing and contain several fragmented pieces of questions from different contexts, such as algebraic equations, electrical engineering principles from Kirchhoff's laws, and optics. However, the very first line 'Find the quotient' suggests that the question is aiming to find the result of a division problem, indicated by concepts such as '12 r 31' which typically refers to a remainder in division. The direct answer can't be delivered due to lack of clarity in the question but it generally involves a division process where you divide a number by 12 and interpret the 'r' as the remainder of this division.
For a clearer step by step explanation in algebra, the standard division calculation step assuming we're dividing a number by 12 to find those respective remainders, we divide the dividend by 12 and determine what the remainder is. If done properly, the answer would be the quotient along with the remainder. As for the other provided equations and statements, they seem to refer to electrical circuit analysis and lens equations from physics, which require different approaches to solve.