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

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

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

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

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

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

Combine like terms: -18n + -6n = -24n
(18 + -24n + 6n2) = 0

Solving
18 + -24n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -4n + n2) = 0

Factor a trinomial.
6((1 + -1n)(3 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
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 = {1, 3}