Solve for variable but variable is still in answer
I try to solve for variable P3. Sage gives me an answer for P3 but it still contains P3 on the right hand side (see last equation after the solve in the beginning of sqrt?
sage: A1, A2, A3, P1, P2, P3, u1, u2, u3, r1, r2, r3, g, C, M1, M2, M3 = var('A1 A2 A3 P1 P2 P3 u1 u2 u3 r1 r2 r3 g C M1 M2 M3')
sage: eq1=A3*(P1-P3)==A3*r3*u3^2-(A2*r2*u2^2+A1*r1*u1^2)
sage: eq2=A3*u3*r3==A2*u2*r2+A1*r1*u1
sage: eq5a=solve([eq2],r3)
sage: eq5b=u3^2+2*g/(g-1)*(P3/(eq5a[0].rhs()))-2*C==0
sage: eq6=solve([eq5b],u3)
sage: eq7a=eq1/A3
sage: eq7b=eq7a.subs(-A3*r3*u3^2 == -(A2*u2*r2+A1*r1*u1)*u3)
sage: eq7b
P1 - P3 == -(A1*r1*u1^2 + A2*r2*u2^2 + (A3*P3*g + sqrt(A3^2*P3^2*g^2 + 2*((g^2 - 2*g + 1)*A1^2*r1^2*u1^2 + 2*(g^2 - 2*g + 1)*A1*A2*r1*r2*u1*u2 + (g^2 - 2*g + 1)*A2^2*r2^2*u2^2)*C))*(A1*r1*u1 + A2*r2*u2)/(A1*(g - 1)*r1*u1 + A2*(g - 1)*r2*u2))/A3
sage: eq7c=eq7b.subs(u3==eq6[0].rhs())
sage: eq7=solve([eq7c],P3)
sage: eq7
[P3 == (A1*r1*u1^2 + A2*r2*u2^2 + A3*P1 - (A1*r1*u1^2 + A2*r2*u2^2 + A3*P1)*g - sqrt(A3^2*P3^2*g^2 + 2*((g^2 - 2*g + 1)*A1^2*r1^2*u1^2 + 2*(g^2 - 2*g + 1)*A1*A2*r1*r2*u1*u2 + (g^2 - 2*g + 1)*A2^2*r2^2*u2^2)*C))/A3]
It looks like it sees P3 and P3 as different variables?
Trying to recreate this gave me an error because eq2 was not defined.
I forgot to copy that line or something, sorry about that