2y2+13y+10=(y+4)2

Rewrite (y+4)2 as (y+4)(y+4).

2y2+13y+10=(y+4)(y+4)

Expand (y+4)(y+4) using the FOIL Method.

Apply the distributive property.

2y2+13y+10=y(y+4)+4(y+4)

Apply the distributive property.

2y2+13y+10=y⋅y+y⋅4+4(y+4)

Apply the distributive property.

2y2+13y+10=y⋅y+y⋅4+4y+4⋅4

2y2+13y+10=y⋅y+y⋅4+4y+4⋅4

Simplify and combine like terms.

Simplify each term.

Multiply y by y.

2y2+13y+10=y2+y⋅4+4y+4⋅4

Move 4 to the left of y.

2y2+13y+10=y2+4⋅y+4y+4⋅4

Multiply 4 by 4.

2y2+13y+10=y2+4y+4y+16

2y2+13y+10=y2+4y+4y+16

Add 4y and 4y.

2y2+13y+10=y2+8y+16

2y2+13y+10=y2+8y+16

2y2+13y+10=y2+8y+16

Subtract y2 from both sides of the equation.

2y2+13y+10-y2=8y+16

Subtract 8y from both sides of the equation.

2y2+13y+10-y2-8y=16

Subtract y2 from 2y2.

y2+13y+10-8y=16

Subtract 8y from 13y.

y2+5y+10=16

y2+5y+10=16

Move 16 to the left side of the equation by subtracting it from both sides.

y2+5y+10-16=0

Subtract 16 from 10.

y2+5y-6=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 -6 and whose sum is 5.

-1,6

Write the factored form using these integers.

(y-1)(y+6)=0

(y-1)(y+6)=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-1=0

y+6=0

Set the first factor equal to 0.

y-1=0

Add 1 to both sides of the equation.

y=1

y=1

Set the next factor equal to 0.

y+6=0

Subtract 6 from both sides of the equation.

y=-6

y=-6

The final solution is all the values that make (y-1)(y+6)=0 true.

y=1,-6

Solve for y 2y^2+13y+10=(y+4)^2