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
