2(n+3)(n-1)=0

Solution for 2(n+3)(n-1)=0 equation:

Simplifying
2(n + 3)(n + -1) = 0

Reorder the terms:
2(3 + n)(n + -1) = 0

Reorder the terms:
2(3 + n)(-1 + n) = 0

Multiply (3 + n) * (-1 + n)
2(3(-1 + n) + n(-1 + n)) = 0
2((-1 * 3 + n * 3) + n(-1 + n)) = 0
2((-3 + 3n) + n(-1 + n)) = 0
2(-3 + 3n + (-1 * n + n * n)) = 0
2(-3 + 3n + (-1n + n2)) = 0

Combine like terms: 3n + -1n = 2n
2(-3 + 2n + n2) = 0
(-3 * 2 + 2n * 2 + n2 * 2) = 0
(-6 + 4n + 2n2) = 0

Solving
-6 + 4n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2n + n2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
n = {-3, 1}