# Solve for y 4y^2+28y+40=0 4y2+28y+40=0
Factor the left side of the equation.
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 by 4 and simplify.
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
y2+7y+10=04
y2+7y+10=04
y2+7y+10=04
Divide 0 by 4.
y2+7y+10=0
y2+7y+10=0
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.
(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 and solve.
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 and solve.
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

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