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

Solution for 2y^2-(y+2)(y-3)=12 equation:

Simplifying
2y2 + -1(y + 2)(y + -3) = 12

Reorder the terms:
2y2 + -1(2 + y)(y + -3) = 12

Reorder the terms:
2y2 + -1(2 + y)(-3 + y) = 12

Multiply (2 + y) * (-3 + y)
2y2 + -1(2(-3 + y) + y(-3 + y)) = 12
2y2 + -1((-3 * 2 + y * 2) + y(-3 + y)) = 12
2y2 + -1((-6 + 2y) + y(-3 + y)) = 12
2y2 + -1(-6 + 2y + (-3 * y + y * y)) = 12
2y2 + -1(-6 + 2y + (-3y + y2)) = 12

Combine like terms: 2y + -3y = -1y
2y2 + -1(-6 + -1y + y2) = 12
2y2 + (-6 * -1 + -1y * -1 + y2 * -1) = 12
2y2 + (6 + 1y + -1y2) = 12

Reorder the terms:
6 + 1y + 2y2 + -1y2 = 12

Combine like terms: 2y2 + -1y2 = 1y2
6 + 1y + 1y2 = 12

Solving
6 + 1y + 1y2 = 12

Solving for variable 'y'.

Reorder the terms:
6 + -12 + 1y + 1y2 = 12 + -12

Combine like terms: 6 + -12 = -6
-6 + 1y + 1y2 = 12 + -12

Combine like terms: 12 + -12 = 0
-6 + 1y + 1y2 = 0

Factor a trinomial.
(-3 + -1y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-3, 2}