4y2+4y-35=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=4⋅-35=-140 and whose sum is b=4.

Factor 4 out of 4y.

4y2+4(y)-35=0

Rewrite 4 as -10 plus 14

4y2+(-10+14)y-35=0

Apply the distributive property.

4y2-10y+14y-35=0

4y2-10y+14y-35=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(4y2-10y)+14y-35=0

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

2y(2y-5)+7(2y-5)=0

2y(2y-5)+7(2y-5)=0

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

(2y-5)(2y+7)=0

(2y-5)(2y+7)=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-5=0

2y+7=0

Set the first factor equal to 0.

2y-5=0

Add 5 to both sides of the equation.

2y=5

Divide each term by 2 and simplify.

Divide each term in 2y=5 by 2.

2y2=52

Cancel the common factor of 2.

Cancel the common factor.

2y2=52

Divide y by 1.

y=52

y=52

y=52

y=52

Set the next factor equal to 0.

2y+7=0

Subtract 7 from both sides of the equation.

2y=-7

Divide each term by 2 and simplify.

Divide each term in 2y=-7 by 2.

2y2=-72

Cancel the common factor of 2.

Cancel the common factor.

2y2=-72

Divide y by 1.

y=-72

y=-72

Move the negative in front of the fraction.

y=-72

y=-72

y=-72

The final solution is all the values that make (2y-5)(2y+7)=0 true.

y=52,-72

The result can be shown in multiple forms.

Exact Form:

y=52,-72

Decimal Form:

y=2.5,-3.5

Mixed Number Form:

y=212,-312

Solve for y 4y^2+4y-35=0