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

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

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

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

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

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

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

Solving
-6 + -1y + y2 = 6

Solving for variable 'y'.

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

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

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

Factor a trinomial.
(-3 + -1y)(4 + -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 '(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
Solution
y = {-3, 4}