3×2-17x-6=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⋅-6=-18 and whose sum is b=-17.

Factor -17 out of -17x.

3×2-17x-6=0

Rewrite -17 as 1 plus -18

3×2+(1-18)x-6=0

Apply the distributive property.

3×2+1x-18x-6=0

Multiply x by 1.

3×2+x-18x-6=0

3×2+x-18x-6=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3×2+x)-18x-6=0

Factor out the greatest common factor (GCF) from each group.

x(3x+1)-6(3x+1)=0

x(3x+1)-6(3x+1)=0

Factor the polynomial by factoring out the greatest common factor, 3x+1.

(3x+1)(x-6)=0

(3x+1)(x-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.

3x+1=0

x-6=0

Set the first factor equal to 0.

3x+1=0

Subtract 1 from both sides of the equation.

3x=-1

Divide each term by 3 and simplify.

Divide each term in 3x=-1 by 3.

3×3=-13

Cancel the common factor of 3.

Cancel the common factor.

3×3=-13

Divide x by 1.

x=-13

x=-13

Move the negative in front of the fraction.

x=-13

x=-13

x=-13

Set the next factor equal to 0.

x-6=0

Add 6 to both sides of the equation.

x=6

x=6

The final solution is all the values that make (3x+1)(x-6)=0 true.

x=-13,6

Solve using the Square Root Property 3x^2-17x-6=0