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

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

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

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

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

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

Combine like terms: 6n + 6n = 12n
(-12 + 12n + -3n2) = 0

Solving
-12 + 12n + -3n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 4n + -1n2) = 0

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

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

Simplifying
-2 + n = 0

Solving
-2 + n = 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 + n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + n = 0 + 2
n = 0 + 2

Combine like terms: 0 + 2 = 2
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}