Solve the Quadratic Equation by factoring. 3r^2-16r-7=5

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