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

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

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

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

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

Multiply (2 + 2n) * (-2 + 6n)
(2(-2 + 6n) + 2n * (-2 + 6n)) = 0
((-2 * 2 + 6n * 2) + 2n * (-2 + 6n)) = 0
((-4 + 12n) + 2n * (-2 + 6n)) = 0
(-4 + 12n + (-2 * 2n + 6n * 2n)) = 0
(-4 + 12n + (-4n + 12n2)) = 0

Combine like terms: 12n + -4n = 8n
(-4 + 8n + 12n2) = 0

Solving
-4 + 8n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 2n + 3n2) = 0

Factor a trinomial.
4((-1 + -1n)(1 + -3n)) = 0

Ignore the factor 4.
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 '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

Solving
1 + -3n = 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 + -3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3n = 0 + -1
-3n = 0 + -1

Combine like terms: 0 + -1 = -1
-3n = -1

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-1, 0.3333333333}