Can someone help explain finance/algebra equations to me? Example:

The CAPM rate is stock return = risk free rate + beta x market premium

If a question asks me to solve for beta, how can I use this equation to solve for it? I'm confused on what happens when you move parts of an equation around and what happens to signs if they switch or not?

An example of a problem with numbers would be this:

A stock has an expected return of 15 percent, the risk-free rate is 5.9 percent, and the market risk premium is 7.7 percent. What must the beta of this stock be? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

A person who answered came up with this explanation:

beta of the stock = (expected return - risk free rate)/(market risk premium

beta of the stock = (15 - 5.9)/7.7 = 1.182

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But I'm confused on how they got that equation for beta and why/how the signs changed?