(n-2)(n+4)=(-3)(3)

Solution for (n-2)(n+4)=(-3)(3) equation:

Simplifying
(n + -2)(n + 4) = (-3)(3)

Reorder the terms:
(-2 + n)(n + 4) = (-3)(3)

Reorder the terms:
(-2 + n)(4 + n) = (-3)(3)

Multiply (-2 + n) * (4 + n)
(-2(4 + n) + n(4 + n)) = (-3)(3)
((4 * -2 + n * -2) + n(4 + n)) = (-3)(3)
((-8 + -2n) + n(4 + n)) = (-3)(3)
(-8 + -2n + (4 * n + n * n)) = (-3)(3)
(-8 + -2n + (4n + n2)) = (-3)(3)

Combine like terms: -2n + 4n = 2n
(-8 + 2n + n2) = (-3)(3)

Multiply -3 * 3
-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}