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

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.

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.

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