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

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

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

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

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

Multiply (-6 + 2n) * (2 + n)
(-6(2 + n) + 2n * (2 + n)) = 0
((2 * -6 + n * -6) + 2n * (2 + n)) = 0
((-12 + -6n) + 2n * (2 + n)) = 0
(-12 + -6n + (2 * 2n + n * 2n)) = 0
(-12 + -6n + (4n + 2n2)) = 0

Combine like terms: -6n + 4n = -2n
(-12 + -2n + 2n2) = 0

Solving
-12 + -2n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1n + n2) = 0

Factor a trinomial.
2((-2 + -1n)(3 + -1n)) = 0

Ignore the factor 2.
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 '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-2, 3}