5y2-42y+16=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=5⋅16=80 and whose sum is b=-42.

Factor -42 out of -42y.

5y2-42y+16=0

Rewrite -42 as -2 plus -40

5y2+(-2-40)y+16=0

Apply the distributive property.

5y2-2y-40y+16=0

5y2-2y-40y+16=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(5y2-2y)-40y+16=0

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

y(5y-2)-8(5y-2)=0

y(5y-2)-8(5y-2)=0

Factor the polynomial by factoring out the greatest common factor, 5y-2.

(5y-2)(y-8)=0

(5y-2)(y-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.

5y-2=0

y-8=0

Set the first factor equal to 0.

5y-2=0

Add 2 to both sides of the equation.

5y=2

Divide each term by 5 and simplify.

Divide each term in 5y=2 by 5.

5y5=25

Cancel the common factor of 5.

Cancel the common factor.

5y5=25

Divide y by 1.

y=25

y=25

y=25

y=25

Set the next factor equal to 0.

y-8=0

Add 8 to both sides of the equation.

y=8

y=8

The final solution is all the values that make (5y-2)(y-8)=0 true.

y=25,8

The result can be shown in multiple forms.

Exact Form:

y=25,8

Decimal Form:

y=0.4,8

Solve for y 5y^2-42y+16=0