# Self Study - How does $\alpha$ and $\beta$ correspond to mean and variance of a beta distribution? [duplicate]

I am trying to figure out how to provide $$\alpha$$ and $$\beta$$ in terms of $$\mu$$ and $$\sigma$$ in a beta distribution.

$$\mu$$ is given as $$\mu = \frac{\alpha}{\alpha + \beta}$$
$$\sigma$$ is given as $$\sigma = \sqrt\frac{\alpha\beta}{(\alpha + \beta)^2(\alpha + \beta + 1)}$$

The author rearranges the formula and arrives at:
$$\alpha = \big(\frac{1 - \mu}{\sigma^2} - \frac{1}{\mu} \big)\mu^2$$
$$\beta = \alpha \big(\frac{1}{\mu} - 1\big)$$

My question is how does he go from $$\mu$$ and $$\sigma$$ formulas to $$\alpha$$ and $$\beta$$? I don't know how to get started even though this seems like such trivial algebra...