6y2-19y+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=-19.

Factor -19 out of -19y.

6y2-19y+8=0

Rewrite -19 as -3 plus -16

6y2+(-3-16)y+8=0

Apply the distributive property.

6y2-3y-16y+8=0

6y2-3y-16y+8=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(6y2-3y)-16y+8=0

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

3y(2y-1)-8(2y-1)=0

3y(2y-1)-8(2y-1)=0

Factor the polynomial by factoring out the greatest common factor, 2y-1.

(2y-1)(3y-8)=0

(2y-1)(3y-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.

2y-1=0

3y-8=0

Set the first factor equal to 0.

2y-1=0

Add 1 to both sides of the equation.

2y=1

Divide each term by 2 and simplify.

Divide each term in 2y=1 by 2.

2y2=12

Cancel the common factor of 2.

Cancel the common factor.

2y2=12

Divide y by 1.

y=12

y=12

y=12

y=12

Set the next factor equal to 0.

3y-8=0

Add 8 to both sides of the equation.

3y=8

Divide each term by 3 and simplify.

Divide each term in 3y=8 by 3.

3y3=83

Cancel the common factor of 3.

Cancel the common factor.

3y3=83

Divide y by 1.

y=83

y=83

y=83

y=83

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

y=12,83

The result can be shown in multiple forms.

Exact Form:

y=12,83

Decimal Form:

y=0.5,2.6‾

Mixed Number Form:

y=12,223

Solve for y 6y^2-19y+8=0