Simplified solution to system of algebraic equations

The following code solves the system of equations for x, but the solution could be further simplified, for example, by factoring N from the numerator. Can I modify the code so the solution is simplified?

syms a b x N g b L m
eqns = [(1/b)*(-2*N*sin(a))/3==m*L, x/b==-(5*L*cos(a))/6+(5*a^2*L*sin(a))/6, N/b==m*(5*L*sin(a))/6+(5*a^2*L)/(6*cos(a) +3*g)]; 
S = solve(eqns,[b m x]);
sol = [S.x] 

Answer 1

[Ameer Hamza]

Try this

syms a b x N g b L m
eqns = [(1/b)*(-2*N*sin(a))/3==m*L, x/b==-(5*L*cos(a))/6+(5*a^2*L*sin(a))/6, N/b==m*(5*L*sin(a))/6+(5*a^2*L)/(6*cos(a) +3*g)]; 
S = solve(eqns,[b m x]);
sol = S.x
sol_simplified = simplify(S.x)

Result:

sol =
-(18*N*cos(a)^2 + 10*N*cos(a)^2*sin(a)^2 + 9*N*g*cos(a) - 18*N*a^2*cos(a)*sin(a) - 5*N*a^2*g*sin(a)^3 + 5*N*g*cos(a)*sin(a)^2 - 10*N*a^2*cos(a)*sin(a)^3 - 9*N*a^2*g*sin(a))/(18*a^2)
 
sol_simplified =
(N*(cos(a) - a^2*sin(a))*(5*cos(a)^2 - 14)*(g + 2*cos(a)))/(18*a^2)

[Aleem Andrew]

Thank you