# Solve for y 6y^2-19y+8=0 6y2-19y+8=0
Factor by grouping.
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 and solve.
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 and solve.
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

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