# Solve for r 3r^2-16r-7=5

3r2-16r-7=5
Move 5 to the left side of the equation by subtracting it from both sides.
3r2-16r-7-5=0
Subtract 5 from -7.
3r2-16r-12=0
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅-12=-36 and whose sum is b=-16.
Factor -16 out of -16r.
3r2-16r-12=0
Rewrite -16 as 2 plus -18
3r2+(2-18)r-12=0
Apply the distributive property.
3r2+2r-18r-12=0
3r2+2r-18r-12=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(3r2+2r)-18r-12=0
Factor out the greatest common factor (GCF) from each group.
r(3r+2)-6(3r+2)=0
r(3r+2)-6(3r+2)=0
Factor the polynomial by factoring out the greatest common factor, 3r+2.
(3r+2)(r-6)=0
(3r+2)(r-6)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
3r+2=0
r-6=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
3r+2=0
Subtract 2 from both sides of the equation.
3r=-2
Divide each term by 3 and simplify.
Divide each term in 3r=-2 by 3.
3r3=-23
Cancel the common factor of 3.
Cancel the common factor.
3r3=-23
Divide r by 1.
r=-23
r=-23
Move the negative in front of the fraction.
r=-23
r=-23
r=-23
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
r-6=0
Add 6 to both sides of the equation.
r=6
r=6
The final solution is all the values that make (3r+2)(r-6)=0 true.
r=-23,6
The result can be shown in multiple forms.
Exact Form:
r=-23,6
Decimal Form:
r=-0.6‾,6
Solve for r 3r^2-16r-7=5

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