[y-3][y+2]=0

Solution for [y-3][y+2]=0 equation:

Simplifying
[y + -3][y + 2] = 0

Reorder the terms:
[-3 + y][y + 2] = 0

Reorder the terms:
[-3 + y][2 + y] = 0

Multiply [-3 + y] * [2 + y]
[-3[2 + y] + y[2 + y]] = 0
[[2 * -3 + y * -3] + y[2 + y]] = 0
[[-6 + -3y] + y[2 + y]] = 0
[-6 + -3y + [2 * y + y * y]] = 0
[-6 + -3y + [2y + y2]] = 0

Combine like terms: -3y + 2y = -1y
[-6 + -1y + y2] = 0

Solving
-6 + -1y + y2 = 0

Solving for variable 'y'.

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-2, 3}