(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 = 0
(-12 + 0 + 3n2) = 0
(-12 + 3n2) = 0

Solving
-12 + 3n2 = 0

Solving for variable 'n'.

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

Add '12' to each side of the equation.
-12 + 12 + 3n2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 3n2 = 0 + 12
3n2 = 0 + 12

Combine like terms: 0 + 12 = 12
3n2 = 12

Divide each side by '3'.
n2 = 4

Simplifying
n2 = 4

Take the square root of each side:
n = {-2, 2}