4y2+28y+40=0

Factor 4 out of 4y2+28y+40.

Factor 4 out of 4y2.

4(y2)+28y+40=0

Factor 4 out of 28y.

4(y2)+4(7y)+40=0

Factor 4 out of 40.

4y2+4(7y)+4⋅10=0

Factor 4 out of 4y2+4(7y).

4(y2+7y)+4⋅10=0

Factor 4 out of 4(y2+7y)+4⋅10.

4(y2+7y+10)=0

4(y2+7y+10)=0

Factor.

Factor y2+7y+10 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 10 and whose sum is 7.

2,5

Write the factored form using these integers.

4((y+2)(y+5))=0

4((y+2)(y+5))=0

Remove unnecessary parentheses.

4(y+2)(y+5)=0

4(y+2)(y+5)=0

4(y+2)(y+5)=0

Divide each term in 4(y+2)(y+5)=0 by 4.

4(y+2)(y+5)4=04

Simplify 4(y+2)(y+5)4.

Cancel the common factor of 4.

Cancel the common factor.

4(y+2)(y+5)4=04

Divide (y+2)(y+5) by 1.

(y+2)(y+5)=04

(y+2)(y+5)=04

Expand (y+2)(y+5) using the FOIL Method.

Apply the distributive property.

y(y+5)+2(y+5)=04

Apply the distributive property.

y⋅y+y⋅5+2(y+5)=04

Apply the distributive property.

y⋅y+y⋅5+2y+2⋅5=04

y⋅y+y⋅5+2y+2⋅5=04

Simplify and combine like terms.

Simplify each term.

Multiply y by y.

y2+y⋅5+2y+2⋅5=04

Move 5 to the left of y.

y2+5⋅y+2y+2⋅5=04

Multiply 2 by 5.

y2+5y+2y+10=04

y2+5y+2y+10=04

Add 5y and 2y.

y2+7y+10=04

y2+7y+10=04

y2+7y+10=04

Divide 0 by 4.

y2+7y+10=0

y2+7y+10=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 10 and whose sum is 7.

2,5

Write the factored form using these integers.

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

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

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

y+2=0

y+5=0

Set the first factor equal to 0.

y+2=0

Subtract 2 from both sides of the equation.

y=-2

y=-2

Set the next factor equal to 0.

y+5=0

Subtract 5 from both sides of the equation.

y=-5

y=-5

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

y=-2,-5

Solve for y 4y^2+28y+40=0