# Solve for y 4y^2+4y-35=0 4y2+4y-35=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=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 and solve.
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 and solve.
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

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