2y2-(y+2)(y-3)=12

Simplify each term.

Apply the distributive property.

2y2+(-y-1⋅2)(y-3)=12

Multiply -1 by 2.

2y2+(-y-2)(y-3)=12

Expand (-y-2)(y-3) using the FOIL Method.

Apply the distributive property.

2y2-y(y-3)-2(y-3)=12

Apply the distributive property.

2y2-y⋅y-y⋅-3-2(y-3)=12

Apply the distributive property.

2y2-y⋅y-y⋅-3-2y-2⋅-3=12

2y2-y⋅y-y⋅-3-2y-2⋅-3=12

Simplify and combine like terms.

Simplify each term.

Multiply y by y by adding the exponents.

Move y.

2y2-(y⋅y)-y⋅-3-2y-2⋅-3=12

Multiply y by y.

2y2-y2-y⋅-3-2y-2⋅-3=12

2y2-y2-y⋅-3-2y-2⋅-3=12

Multiply -3 by -1.

2y2-y2+3y-2y-2⋅-3=12

Multiply -2 by -3.

2y2-y2+3y-2y+6=12

2y2-y2+3y-2y+6=12

Subtract 2y from 3y.

2y2-y2+y+6=12

2y2-y2+y+6=12

2y2-y2+y+6=12

Subtract y2 from 2y2.

y2+y+6=12

y2+y+6=12

Move 12 to the left side of the equation by subtracting it from both sides.

y2+y+6-12=0

Subtract 12 from 6.

y2+y-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 1.

-2,3

Write the factored form using these integers.

(y-2)(y+3)=0

(y-2)(y+3)=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+3=0

Set the first factor equal to 0.

y-2=0

Add 2 to both sides of the equation.

y=2

y=2

Set the next factor equal to 0.

y+3=0

Subtract 3 from both sides of the equation.

y=-3

y=-3

The final solution is all the values that make (y-2)(y+3)=0 true.

y=2,-3

Solve for y 2y^2-(y+2)(y-3)=12