Why is it that if you have this equation $\displaystyle (log6+logx)logx = 3$, the result would become $\displaystyle (logx)^2+(log6)logx-3=0$ I don't understand why the logx squares.
When you distribute the $\displaystyle \log(x)$ to the two terms within the parentheses, one of the resulting terms is $\displaystyle \log^2(x)$.
For example, if you have $\displaystyle (x+y)y$ distributing the $\displaystyle y$ gives $\displaystyle xy+y^2$.