solve x^2+y^2+z^2 = 1, 2*(m*x+n*y+p*z) = -3, 2*(m*y+n*z+p*x) = 0, m^2+n^2+p^2+2*(x*y+x*z+y*z) = 2, 2*(m*n+m*p+m*z+n*p+n*x+p*y) = 0, x+y+z+m+n+p = 0