(y-2)(y+3)-6=0

Solution for (y-2)(y+3)-6=0 equation:

Simplifying
(y + -2)(y + 3) + -6 = 0

Reorder the terms:
(-2 + y)(y + 3) + -6 = 0

Reorder the terms:
(-2 + y)(3 + y) + -6 = 0

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

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

Reorder the terms:
-6 + -6 + 1y + y2 = 0

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

Solving
-12 + 1y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -1y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4
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 = {-4, 3}