I have to find $f(x,y,z)=24xyz$ maximum value on surface $8x+3y+6z=21$. I have found the partial derivatives of $f$ and used Langranian to form
$$8x+3y+6z=21\\ 24yz=\lambda 8\\ 24xz=\lambda 3\\ 24xy=\lambda 6$$
So, my problem is that how can I solve the points $x$,$y$,$x$ and Langrange multiplier $\lambda$ to find the maximum point?
Thanks for your answers in advance!