6×2-13x-8=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⋅-8=-48 and whose sum is b=-13.

Factor -13 out of -13x.

6×2-13x-8=0

Rewrite -13 as 3 plus -16

6×2+(3-16)x-8=0

Apply the distributive property.

6×2+3x-16x-8=0

6×2+3x-16x-8=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(6×2+3x)-16x-8=0

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

3x(2x+1)-8(2x+1)=0

3x(2x+1)-8(2x+1)=0

Factor the polynomial by factoring out the greatest common factor, 2x+1.

(2x+1)(3x-8)=0

(2x+1)(3x-8)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

2x+1=0

3x-8=0

Set the first factor equal to 0.

2x+1=0

Subtract 1 from 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

Move the negative in front of the fraction.

x=-12

x=-12

x=-12

Set the next factor equal to 0.

3x-8=0

Add 8 to both sides of the equation.

3x=8

Divide each term by 3 and simplify.

Divide each term in 3x=8 by 3.

3×3=83

Cancel the common factor of 3.

Cancel the common factor.

3×3=83

Divide x by 1.

x=83

x=83

x=83

x=83

The final solution is all the values that make (2x+1)(3x-8)=0 true.

x=-12,83

Solve Using the Square Root Property 6x^2-13x-8=0