k6=6*r, 

k5=-15*r^2+6*b*h*m+6*c*g*m+3*d^2*m, 

k4=20*r^3+m*(g*(6*b^2-24*c*r)-24*b*h*r-12*d^2*r+12*b*c*d+2*c^3)+(6*c*h^2+12*d*g*h+2*g^3)*m^2, 

k3=-15*r^4+m*(g*(36*c*r^2-18*b^2*r)+36*b*h*r^2+18*d^2*r^2+d*(6*b^3-36*b*c*r)-6*c^3*r+9*b^2*c^2)+m^2*(h*(18*c^2*d-36*d*g*r)+h^2*(-18*c*r-9*b^2)-6*g^3*r+ 

   (18*b*d-9*c^2)*g^2-3*d^4)+(6*d*h^3+9*g^2*h^2)*m^3, 

k2=6*r^5+m*(g*(18*b^2*r^2-24*c*r^3)-24*b*h*r^3-12*d^2*r^3+d*(36*b*c*r^2-12*b^3*r)+6*c^3*r^2-18*b^2*c^2*r+6*b^4*c)+m^2*(h*(g*(36*d*r^2-12*b^3)-36*c^2*d*r+

   12*b*c^3)+h^2*(18*c*r^2+18*b^2*r)+6*g^3*r^2+g^2*(18*c^2*r-36*b*d*r)+6*d^4*r+(18*b^2*d^2-6*c^4)*g-12*b*c*d^3+6*c^3*d^2)+m^3*(h^2*(18*c*d^2-18*g^2*r)+

   h^3*(-12*d*r-12*b*c)+(12*b*g^3-12*d^3*g)*h-6*c*g^4+6*d^2*g^3)+6*g*h^4*m^4, 

k1=-r^6+m*(-g*(6*b^2*r^3-6*c*r^4)+6*b*h*r^4+3*d^2*r^4-d*(12*b*c*r^3-6*b^3*r^2)-2*c^3*r^3+9*b^2*c^2*r^2-6*b^4*c*r+b^6)+m^2*(-h*(g*(12*d*r^3-12*b^3*r)+

   d*(6*b^4-18*c^2*r^2)+12*b*c^3*r-6*b^3*c^2)-h^2*(6*c*r^3+9*b^2*r^2)-2*g^3*r^3-g^2*(-18*b*d*r^2+9*c^2*r^2+3*b^4)-3*d^4*r^2-g*(18*b^2*d^2*r-6*c^4*r-

   12*b^3*c*d+6*b^2*c^3)-d^2*(6*c^3*r+9*b^2*c^2)-d^3*(-12*b*c*r-2*b^3)+6*b*c^4*d-c^6)+m^3*(-h^2*(-9*g^2*r^2+d^2*(18*c*r-9*b^2)+18*b^2*c*g-3*c^4)-

   h^3*(-6*d*r^2-12*b*c*r-2*b^3)-h*(g*(12*c^3*d-12*d^3*r)+12*b*g^3*r-18*b*c^2*g^2+6*b*d^4-6*c^2*d^3)-g^3*(6*d^2*r+12*b*c*d+2*c^3)-g^4*(-6*c*r-3*b^2)-

   (-6*b*d^3-9*c^2*d^2)*g^2-6*c*d^4*g+d^6)-m^4*(h^4*(6*g*r+6*b*d+3*c^2)+(-6*b*g^2-12*c*d*g-2*d^3)*h^3+(6*c*g^3+9*d^2*g^2)*h^2-6*d*g^4*h+g^6)+h^6*m^5,

for the polynomial x^6-k6*x^5-k5*x^4-k4*x^3-k3*x^2-k2*x-k1,

roots:

x1=r+h*m^(5/6)+g*m^(2/3)+d*sqrt(m)+c*m^(1/3)+b*m^(1/6),

x2=r-h*m^(5/6)+g*m^(2/3)-d*sqrt(m)+c*m^(1/3)-b*m^(1/6),

x3=r+((sqrt(3)*%i+1)*h*m^(5/6))/2+((sqrt(3)*%i-1)*g*m^(2/3))/2-d*sqrt(m)-((sqrt(3)*%i+1)*c*m^(1/3))/2-((sqrt(3)*%i-1)*b*m^(1/6))/2,

x4=r+((sqrt(3)*%i-1)*h*m^(5/6))/2-((sqrt(3)*%i+1)*g*m^(2/3))/2+d*sqrt(m)+((sqrt(3)*%i-1)*c*m^(1/3))/2-((sqrt(3)*%i+1)*b*m^(1/6))/2,

x5=r-((sqrt(3)*%i+1)*h*m^(5/6))/2+((sqrt(3)*%i-1)*g*m^(2/3))/2+d*sqrt(m)-((sqrt(3)*%i+1)*c*m^(1/3))/2+((sqrt(3)*%i-1)*b*m^(1/6))/2,

x6=r-((sqrt(3)*%i-1)*h*m^(5/6))/2-((sqrt(3)*%i+1)*g*m^(2/3))/2-d*sqrt(m)+((sqrt(3)*%i-1)*c*m^(1/3))/2+((sqrt(3)*%i+1)*b*m^(1/6))/2.