14n^2+62n+30=6

Solution for 14n^2+62n+30=6 equation:

Simplifying
14n2 + 62n + 30 = 6

Reorder the terms:
30 + 62n + 14n2 = 6

Solving
30 + 62n + 14n2 = 6

Solving for variable 'n'.

Reorder the terms:
30 + -6 + 62n + 14n2 = 6 + -6

Combine like terms: 30 + -6 = 24
24 + 62n + 14n2 = 6 + -6

Combine like terms: 6 + -6 = 0
24 + 62n + 14n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 31n + 7n2) = 0

Factor a trinomial.
2((4 + n)(3 + 7n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(3 + 7n)' equal to zero and attempt to solve:

Simplifying
3 + 7n = 0

Solving
3 + 7n = 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 + 7n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7n = 0 + -3
7n = 0 + -3

Combine like terms: 0 + -3 = -3
7n = -3

Divide each side by '7'.
n = -0.4285714286

Simplifying
n = -0.4285714286
Solution
n = {-4, -0.4285714286}