I have worked an equation as low as i can. I need help to solve for a variable.

I have been working on a problem in which I have been working for hours to no avail. This is something i'll be putting into python, but can't seem to figure the end result here.

Original variables look like this initially: $$\frac{(Fa \times Op) + (Ca \times Cp)}{Fa + Ca} = Np$$ I did this to help simplify it down. $$Fa = A$$, $$Op = B$$, $$Ca = C$$, $$Cp = D$$, $$Np = E$$

Which looks like: $$\frac{(A \times B) + (C \times D)}{A + C} = E$$

I'm trying to set an equation for each variable. I NEED TO SOLVE for A(Fa) as well as for E(Np) relative to the equations. Any other equations I could get such as solving for B,C,D would be just used to verify my A,F equations. Please I could really use the help. I've been over this many hours and my math isn't stacking up.

• There's no point in giving two sets of variables, so please just use $\frac{AB+CD}{A+C}=E$. In this case it seems like you've already solved for $E$. If you need to solve for $A$, then cross multiplication gives $AB+CD = E(A+C)$ and rearranging gives $AB-AE = CE - CD$ and dividing by $B-E$ gives $A = \frac{CE-CD}{B-E}$. – sfmiller940 Apr 15 at 18:56