How do you solve by factoring and using the principle of zero products ##36r^2=16##?

##r=2/3## ##r=-2/3##

##36r^2=16##

Make one side equal to zero by subtracting 16 from each side: ##36r^2-16=0##

First, I would factor out a ##4## so that I'm working with smaller numbers: ##4(9r^2-4)=0##

Use the property that: ##a^2-b^2=(a+b)(a-b)##

##4[(3r)^2-(2)^2]=0##

##4(3r-2)(3r+2)=0##

Set each factor (apart from constants) equal to zero individually. ##3r-2=0## ##3r=2## ##r=2/3##

##3r+2=0## ##3r=-2## ##r=-2/3##