12n^2+10n+2=0

Solution for 12n^2+10n+2=0 equation:

Simplifying
12n2 + 10n + 2 = 0

Reorder the terms:
2 + 10n + 12n2 = 0

Solving
2 + 10n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 5n + 6n2) = 0

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

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

Simplifying
1 + 2n = 0

Solving
1 + 2n = 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 + 2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2n = 0 + -1
2n = 0 + -1

Combine like terms: 0 + -1 = -1
2n = -1

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
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 = {-0.5, -0.3333333333}