(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 = -10n
(12 + -10n + 2n2) = 0

Solving
12 + -10n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -5n + 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}