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

Solution for (y-2)(y+3)=0 equation:

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

Reorder the terms:
(-2 + y)(y + 3) = 0

Reorder the terms:
(-2 + y)(3 + y) = 0

Multiply (-2 + y) * (3 + y)
(-2(3 + y) + y(3 + y)) = 0
((3 * -2 + y * -2) + y(3 + y)) = 0
((-6 + -2y) + y(3 + y)) = 0
(-6 + -2y + (3 * y + y * y)) = 0
(-6 + -2y + (3y + y2)) = 0

Combine like terms: -2y + 3y = 1y
(-6 + 1y + y2) = 0

Solving
-6 + 1y + y2 = 0

Solving for variable 'y'.

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}