6×2-13x+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=6⋅6=36 and whose sum is b=-13.

Factor -13 out of -13x.

6×2-13x+6=0

Rewrite -13 as -4 plus -9

6×2+(-4-9)x+6=0

Apply the distributive property.

6×2-4x-9x+6=0

6×2-4x-9x+6=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(6×2-4x)-9x+6=0

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

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

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

Factor the polynomial by factoring out the greatest common factor, 3x-2.

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

(3x-2)(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-2=0

2x-3=0

Set the first factor equal to 0.

3x-2=0

Add 2 to both sides of the equation.

3x=2

Divide each term by 3 and simplify.

Divide each term in 3x=2 by 3.

3×3=23

Cancel the common factor of 3.

Cancel the common factor.

3×3=23

Divide x by 1.

x=23

x=23

x=23

x=23

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-2)(2x-3)=0 true.

x=23,32

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