(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.
(-4 + -1y)(5 + -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 '(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 = {-4, 5}