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...

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