If i'm given a firm's production function of
$$Y=zK^{\alpha}{N}^{1-\alpha}.$$
Then assuming $K$ is fixed and cost free, we can get our profit maximization problem of
$$\max_{{N}}zF(K^{\alpha}{N}^{1-\alpha})-wN.$$
To find the optimality condition, ${MP}_{N}=w$ , I take the partial derivative and find
$$z{F}_{N}=z(1-\alpha){K}^{\alpha}{N}^{-\alpha}=w.$$
Here is where I'm stuck.
I need to show that the optimality condition can be written as $\alpha=1-\frac{wN}{Y}$.