(y+3)(y-2)=14

Solution for (y+3)(y-2)=14 equation:

Simplifying
(y + 3)(y + -2) = 14

Reorder the terms:
(3 + y)(y + -2) = 14

Reorder the terms:
(3 + y)(-2 + y) = 14

Multiply (3 + y) * (-2 + y)
(3(-2 + y) + y(-2 + y)) = 14
((-2 * 3 + y * 3) + y(-2 + y)) = 14
((-6 + 3y) + y(-2 + y)) = 14
(-6 + 3y + (-2 * y + y * y)) = 14
(-6 + 3y + (-2y + y2)) = 14

Combine like terms: 3y + -2y = 1y
(-6 + 1y + y2) = 14

Solving
-6 + 1y + y2 = 14

Solving for variable 'y'.

Reorder the terms:
-6 + -14 + 1y + y2 = 14 + -14

Combine like terms: -6 + -14 = -20
-20 + 1y + y2 = 14 + -14

Combine like terms: 14 + -14 = 0
-20 + 1y + y2 = 0

Factor a trinomial.
(-5 + -1y)(4 + -1y) = 0

Subproblem 1
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
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 = {-5, 4}