<s>[INST] Why is $2x-1=7$ not $x=-4 \text{ or } x=4$ How would you explain why $3(2x-1)^2=147$, is $2x-1=7 \text{ or } 2x-1=-7$. But not $2x=8 \text{ so } x=4 \text{ or } x=-4$? 
 [/INST] $$3\left(2x-1\right)^{2}=147\iff\left(2x-1\right)^{2}-49=0\iff$$$$\left[\left(2x-1\right)-7\right]\left[\left(2x-1\right)+7\right]=0\iff\left(2x-8\right)\left(2x+6\right)=0$$
A product $p\times q$ equals $0$ if and only if $p=0$ or $q=0$.
Applying that here gives $2x-8=0$ or $2x+6=0$.
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