2n^2-12n+2=-8

Solution for 2n^2-12n+2=-8 equation:

Simplifying
2n2 + -12n + 2 = -8

Reorder the terms:
2 + -12n + 2n2 = -8

Solving
2 + -12n + 2n2 = -8

Solving for variable 'n'.

Reorder the terms:
2 + 8 + -12n + 2n2 = -8 + 8

Combine like terms: 2 + 8 = 10
10 + -12n + 2n2 = -8 + 8

Combine like terms: -8 + 8 = 0
10 + -12n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -6n + n2) = 0

Factor a trinomial.
2((1 + -1n)(5 + -1n)) = 0

Ignore the factor 2.
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 '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {1, 5}