Question

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

Answer 1

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