(2n-4)(3n-6)=0

Solution for (2n-4)(3n-6)=0 equation:

Simplifying
(2n + -4)(3n + -6) = 0

Reorder the terms:
(-4 + 2n)(3n + -6) = 0

Reorder the terms:
(-4 + 2n)(-6 + 3n) = 0

Multiply (-4 + 2n) * (-6 + 3n)
(-4(-6 + 3n) + 2n * (-6 + 3n)) = 0
((-6 * -4 + 3n * -4) + 2n * (-6 + 3n)) = 0
((24 + -12n) + 2n * (-6 + 3n)) = 0
(24 + -12n + (-6 * 2n + 3n * 2n)) = 0
(24 + -12n + (-12n + 6n2)) = 0

Combine like terms: -12n + -12n = -24n
(24 + -24n + 6n2) = 0

Solving
24 + -24n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + -4n + n2) = 0

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

Ignore the factor 6.
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 '(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
Solution
n = {2, 2}