6×2-7x-3=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⋅-3=-18 and whose sum is b=-7.

Factor -7 out of -7x.

6×2-7x-3=0

Rewrite -7 as 2 plus -9

6×2+(2-9)x-3=0

Apply the distributive property.

6×2+2x-9x-3=0

6×2+2x-9x-3=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(6×2+2x)-9x-3=0

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

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

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

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

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

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

Add 3 to both sides of the equation.

2x=3

Divide each term by 2 and simplify.

Divide each term in 2x=3 by 2.

2×2=32

Cancel the common factor of 2.

Cancel the common factor.

2×2=32

Divide x by 1.

x=32

x=32

x=32

x=32

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

x=-13,32

Solve Using the Square Root Property 6x^2-7x-3=0