72n^2+24n+2=0

Solution for 72n^2+24n+2=0 equation:

Simplifying
72n2 + 24n + 2 = 0

Reorder the terms:
2 + 24n + 72n2 = 0

Solving
2 + 24n + 72n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 12n + 36n2) = 0

Factor a trinomial.
2((1 + 6n)(1 + 6n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 6n)' equal to zero and attempt to solve:

Simplifying
1 + 6n = 0

Solving
1 + 6n = 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 + 6n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6n = 0 + -1
6n = 0 + -1

Combine like terms: 0 + -1 = -1
6n = -1

Divide each side by '6'.
n = -0.1666666667

Simplifying
n = -0.1666666667
Subproblem 2
Set the factor '(1 + 6n)' equal to zero and attempt to solve:

Simplifying
1 + 6n = 0

Solving
1 + 6n = 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 + 6n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6n = 0 + -1
6n = 0 + -1

Combine like terms: 0 + -1 = -1
6n = -1

Divide each side by '6'.
n = -0.1666666667

Simplifying
n = -0.1666666667
Solution
n = {-0.1666666667, -0.1666666667}