(y+3)(y-2)=24

Solution for (y+3)(y-2)=24 equation:

Simplifying
(y + 3)(y + -2) = 24

Reorder the terms:
(3 + y)(y + -2) = 24

Reorder the terms:
(3 + y)(-2 + y) = 24

Multiply (3 + y) * (-2 + y)
(3(-2 + y) + y(-2 + y)) = 24
((-2 * 3 + y * 3) + y(-2 + y)) = 24
((-6 + 3y) + y(-2 + y)) = 24
(-6 + 3y + (-2 * y + y * y)) = 24
(-6 + 3y + (-2y + y2)) = 24

Combine like terms: 3y + -2y = 1y
(-6 + 1y + y2) = 24

Solving
-6 + 1y + y2 = 24

Solving for variable 'y'.

Reorder the terms:
-6 + -24 + 1y + y2 = 24 + -24

Combine like terms: -6 + -24 = -30
-30 + 1y + y2 = 24 + -24

Combine like terms: 24 + -24 = 0
-30 + 1y + y2 = 0

Factor a trinomial.
(-6 + -1y)(5 + -1y) = 0

Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

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

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

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-6, 5}