(N-6)(N+2)=0

Solution for (N-6)(N+2)=0 equation:

Simplifying
(N + -6)(N + 2) = 0

Reorder the terms:
(-6 + N)(N + 2) = 0

Reorder the terms:
(-6 + N)(2 + N) = 0

Multiply (-6 + N) * (2 + N)
(-6(2 + N) + N(2 + N)) = 0
((2 * -6 + N * -6) + N(2 + N)) = 0
((-12 + -6N) + N(2 + N)) = 0
(-12 + -6N + (2 * N + N * N)) = 0
(-12 + -6N + (2N + N2)) = 0

Combine like terms: -6N + 2N = -4N
(-12 + -4N + N2) = 0

Solving
-12 + -4N + N2 = 0

Solving for variable 'N'.

Factor a trinomial.
(-2 + -1N)(6 + -1N) = 0

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

Simplifying
-2 + -1N = 0

Solving
-2 + -1N = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1N = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1N = 0 + 2
-1N = 0 + 2

Combine like terms: 0 + 2 = 2
-1N = 2

Divide each side by '-1'.
N = -2

Simplifying
N = -2
Subproblem 2
Set the factor '(6 + -1N)' equal to zero and attempt to solve:

Simplifying
6 + -1N = 0

Solving
6 + -1N = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1N = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1N = 0 + -6
-1N = 0 + -6

Combine like terms: 0 + -6 = -6
-1N = -6

Divide each side by '-1'.
N = 6

Simplifying
N = 6
Solution
N = {-2, 6}