6×2-x-1=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=6⋅-1=-6 and whose sum is b=-1.
Factor -1 out of -x.
6×2-(x)-1=0
Rewrite -1 as 2 plus -3
6×2+(2-3)x-1=0
Apply the distributive property.
6×2+2x-3x-1=0
6×2+2x-3x-1=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(6×2+2x)-3x-1=0
Factor out the greatest common factor (GCF) from each group.
2x(3x+1)-(3x+1)=0
2x(3x+1)-(3x+1)=0
Factor the polynomial by factoring out the greatest common factor, 3x+1.
(3x+1)(2x-1)=0
(3x+1)(2x-1)=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
2x-1=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.
2x-1=0
Add 1 to both sides of the equation.
2x=1
Divide each term by 2 and simplify.
Divide each term in 2x=1 by 2.
2×2=12
Cancel the common factor of 2.
Cancel the common factor.
2×2=12
Divide x by 1.
x=12
x=12
x=12
x=12
The final solution is all the values that make (3x+1)(2x-1)=0 true.
x=-13,12
Solve Using the Square Root Property 6x^2-x-1=0
