Nothing is done arbitrary, there is a logic behind it.

g = b/4a

We want to isolate 'a' to the left hand side of the equation.

First, both sides are multiplied by '4a'

4a*g=(4a)*(b/4a)

4ag = b

Then both sides are divided by '4g' so that there is only 'a' left:

(4ag)/(4g) = b/(4g)

a = b/(4g)

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