(n+4)(n-2)=-9

Solution for (n+4)(n-2)=-9 equation:

Simplifying
(n + 4)(n + -2) = -9

Reorder the terms:
(4 + n)(n + -2) = -9

Reorder the terms:
(4 + n)(-2 + n) = -9

Multiply (4 + n) * (-2 + n)
(4(-2 + n) + n(-2 + n)) = -9
((-2 * 4 + n * 4) + n(-2 + n)) = -9
((-8 + 4n) + n(-2 + n)) = -9
(-8 + 4n + (-2 * n + n * n)) = -9
(-8 + 4n + (-2n + n2)) = -9

Combine like terms: 4n + -2n = 2n
(-8 + 2n + n2) = -9

Solving
-8 + 2n + n2 = -9

Solving for variable 'n'.

Reorder the terms:
-8 + 9 + 2n + n2 = -9 + 9

Combine like terms: -8 + 9 = 1
1 + 2n + n2 = -9 + 9

Combine like terms: -9 + 9 = 0
1 + 2n + n2 = 0

Factor a trinomial.
(1 + n)(1 + n) = 0

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

Simplifying
n = -1
Solution
n = {-1, -1}