so first set one side to zero
subtract 5 from both sides
3r^2-16r-12=0
factor
to find the factor in
ax^2+bx+c form when a>1
multiply a and c together
find what 2 numbers add up to b and multiply to ac so
a=3
b=-16
c=-12
ac=3 times -12=-36
factors that add up to -16
2 and -18 is the answer since 2 times -18=-36 and 2-18=-16 so
split the middle number up
3r^2-16r-12=0
3r^2-18r+2r-12=0
group
(3r^2-18r)+(2r-12)=0
factor out common factors
(3r)(r-6)+(2)(r-6)=0
reverse distribute (ab+ac=a(b+c) so
(3r+2)(r-6)=0
set each to zero
r-6=0
add 6
r=6
3r+2=0
subtract 2
3r=-2
divide 3
r=-2/3
r=6 or -2/3
