Math Help - Solve for F

S + E(P) = (S+P) (F) + (S+B) (1-F)

-So I need to solve for F and what I mostly struggle with is the fact that multiple variables appear multiple times
- I am guessing you would subtract (S+P) and (S-B) from the left hand side first???
- Then, F+ (1-F) = F???
- Last combine like terms on the left hand side??

I am pretty sure I am doing it wrong, or at least I arrive at the wrong answer. All I am really interested in is what are the steps for solving a problem like this? Thanks.

Please feel free to include any articles/vids on the subject as well. Thanks.

You cannot subtract S + P or S + B first because they are connected to an expression in F by multiplication. The correct undue operation would be division. However, that will make the problem very really to finish. Foil all products first. For (S + P) F, distribute the F to S and then P and then add them. For (S + B) (1 - F) similar thing.

S + E(P) = (S + P) F + (S + B) (1 - F)
S + E * P = S * F + P * F + S * (1 - F) + B * (1 - F)
S + E * P = S * F + P * F + S - S * F + B - B * F
S + E * P = P * F + S + B - B * F

Now we want the F to one side. Then we want F all by itself. Subtract S + B from both sides.

E * P - B = P * F - B * F

Factor F from the right side

E * P - B = (P - B) * F

Divide both sides by P - B.

(E * P - B) / (P - B) = F

Hey, not sure I understand line 3(S + E * P = S * F + P * F + S - S * F + B - B * F) Where is the -S and -B coming from???

I also noticed you arrived at the wrong answer, it should be +B instead of -B, maybe you made an error, could you take a second look? It is possible I entered in the wrong equality, I will double check that as well.

Anyway, thanks for the attempt!

Mathguy's answer is definitely correct from what you gave.

It's easier to see where the -S and -B came from when written down.