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

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

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

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

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

Multiply (-6 + 2n) * (-6 + 3n)
(-6(-6 + 3n) + 2n * (-6 + 3n)) = 0
((-6 * -6 + 3n * -6) + 2n * (-6 + 3n)) = 0
((36 + -18n) + 2n * (-6 + 3n)) = 0
(36 + -18n + (-6 * 2n + 3n * 2n)) = 0
(36 + -18n + (-12n + 6n2)) = 0

Combine like terms: -18n + -12n = -30n
(36 + -30n + 6n2) = 0

Solving
36 + -30n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + -5n + n2) = 0

Factor a trinomial.
6((2 + -1n)(3 + -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 '(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}