In general, it is impossible to solve the equation f(x_1,...,x_12)*g(x_1)=Lambda for x_1. Symbolic math software (such as Mathematica or the free version at WolframAlpha.com) can invert simple equations such as low-order polynomials, and I think that is what you are asking about. No, SAS does not contain a symbolic algebra system.
However, for any specified value of Lambda, you can NUMERICALLY solve for the value of x_1 that satisfies the equation by finding the root (zero) of the equation f(x_1,...,x_12)*g(x_1) - Lambda = 0. This is a one-dimensional root-finding problem, so can be solved in many ways. See
Find the root by using the DATA step
Find the root in SAS/IML by using the FROOT function
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