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

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

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

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

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

Multiply (3 + n) * (-2 + n)
(3(-2 + n) + n(-2 + n)) = 14
((-2 * 3 + n * 3) + n(-2 + n)) = 14
((-6 + 3n) + n(-2 + n)) = 14
(-6 + 3n + (-2 * n + n * n)) = 14
(-6 + 3n + (-2n + n2)) = 14

Combine like terms: 3n + -2n = 1n
(-6 + 1n + n2) = 14

Solving
-6 + 1n + n2 = 14

Solving for variable 'n'.

Reorder the terms:
-6 + -14 + 1n + n2 = 14 + -14

Combine like terms: -6 + -14 = -20
-20 + 1n + n2 = 14 + -14

Combine like terms: 14 + -14 = 0
-20 + 1n + n2 = 0

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

Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

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

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

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

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

Simplifying
n = -5
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

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

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

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

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

Simplifying
n = 4
Solution
n = {-5, 4}