IF ((K*Q)*30)+Q=U and I have U and K how do I solve Q? (30 is a constant)

Question

This is easy for me to figure out: ((K*Q)*30)+Q=U
K (property tax percentage)
Q (initial cost of the house)
30 refers to 30 years
U is the solution, the total cost to buy the house after the initial down payment and the 30 years of property taxes (assuming the home value does not go up)

This is what I need help on: (If I know U and K and the number 30 remains 30, then how can I derive Q mathematically?)

Another way to ask the question is below:

CALCULATION A (I can do)
K (the tax rate in each town)
* (times)
Q (the cost to buy the house from the seller)
= R (the resulting annual tax to own the house)

CALCULATION B (I can do)
R (from above)
* (times)
30 (years) = T (the 30 year tax to own the house)

CALCULATION C (I can do)
T (the 30 year tax to own the house)
+ (plus)
Q (the initial cost of the house)
= U (TOTAL COST OF OWNERSHIP [the 30 year tax plus the cost of the house])

With these calculations if I know K (the tax rate in each town) and if I know Q (the cost to buy the house now) I can calculate U (the total amount it would have cost me after 30 years)

CALCULATION D (I don't know how to do)
Now I would like a new formula where if I decide in advance the value for U and if I know the value K then I can *solve* a value for Q

Answer 1

I treated this like an algebraic expression.  You gave the formula ((K*Q)*30)+Q=U.  That's the same things as U=(30KQ)+Q.

 

If you solve this for Q, you'd get Q= U/30K+1.

 

Hope this helps!