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##