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

2y2-(y+2)(y-3)=12
Simplify 2y2-(y+2)(y-3).
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
Factor y2+y-6 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 -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 and solve.
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 and solve.
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

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