Solving a nasty equation with 17 variables...

I need to solve the following equation for "R." All variables are single letters. Please help, I've been working at it for days now and just can't get it (Worried)

I+(O*M*K*R*T) =

{J*[(A/B)+((C-D)/B)]*{[(E*B)+(N*M*G*T*B*R)-(F*A)]/[F(C-D)-B(G-H)]}} - {(K-L)*[(E*B)+(N*M*G*T*B*R)-(B*A)]/[F(C-D)-B(G-H)]}

I know that's hell to read. Any suggestions of a better way to present it would be much apprecaited. Please feel free to ask questions if you need clarification.

Thank you SO SO SO much!

Cheers,

ChemOsh (Worried)

Re: Solving a nasty equation with 17 variables...

What do you **mean** by "solve" it? There exist an infinite set of values that will solve it. With one equation in 17 variables, the best you can do is solve for one of the variables in terms of the other 16.

Re: Solving a nasty equation with 17 variables...

If it’s a matrix equation, with division meaning mult. by inverse,

R = K^{-1} M^{-1} O^{-1} {{ }-I} T^{-1}, assuming all operations work.

Re: Solving a nasty equation with 17 variables...

your equation becomes easier to read if you replace formulas that don't involve R with a single letter. for example, let:

S = J*[(A/B)+(C-D)/B)]

U = N*M*G*T*B

V = F(C-D) - B(G-H)

W = O*M*K*T (assuming multiplication is commutative, so R*T = T*R)

this gives us I + W*R = S*[(E-B) + U*R - (F*A)]/V - (K-L)*[(E-B) + U*R - (B*A)]/V

so W*R = (S*U)*R/V - [(K-L)*U]*R/V + (S*(E-B))/V - [S*(F*A)]/V - [(K-L)*(E-B)]/V + [(K-L)*(B*A)]/V - I

the entire expression (S*(E-B))/V - [S*(F*A)]/V - [(K-L)*(E-B)]/V + [(K-L)*(B*A)]/V - I does not involve R, so we can call it X:

W*R = [(S*U) - (K-L)*U]*R/V + X

and letting Y = [(S*U) - (K-L)*U]/V we have:

W*R = Y*R + X, so

(W-Y)*R = X and

R = X/(W-Y) (assuming that W-Y is non-zero, which has to be checked separately).

the back-substitution is going to get REALLY messy, and i doubt there will be much cancellation.

Re: Solving a nasty equation with 17 variables...

If you group Letters and do some simple algebra:

k1R = k2R + K3

EDIT: Actually same reasoning applies if letters are matrices, assuming all operations are defined