(y-5)(y-2)=28

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

Apply the distributive property.

y(y-2)-5(y-2)=28

Apply the distributive property.

y⋅y+y⋅-2-5(y-2)=28

Apply the distributive property.

y⋅y+y⋅-2-5y-5⋅-2=28

y⋅y+y⋅-2-5y-5⋅-2=28

Simplify and combine like terms.

Simplify each term.

Multiply y by y.

y2+y⋅-2-5y-5⋅-2=28

Move -2 to the left of y.

y2-2⋅y-5y-5⋅-2=28

Multiply -5 by -2.

y2-2y-5y+10=28

y2-2y-5y+10=28

Subtract 5y from -2y.

y2-7y+10=28

y2-7y+10=28

y2-7y+10=28

Move 28 to the left side of the equation by subtracting it from both sides.

y2-7y+10-28=0

Subtract 28 from 10.

y2-7y-18=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 -18 and whose sum is -7.

-9,2

Write the factored form using these integers.

(y-9)(y+2)=0

(y-9)(y+2)=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-9=0

y+2=0

Set the first factor equal to 0.

y-9=0

Add 9 to both sides of the equation.

y=9

y=9

Set the next factor equal to 0.

y+2=0

Subtract 2 from both sides of the equation.

y=-2

y=-2

The final solution is all the values that make (y-9)(y+2)=0 true.

y=9,-2

Solve using the Square Root Property (y-5)(y-2)=28