14n^2+55n+21=0

Solution for 14n^2+55n+21=0 equation:

Simplifying
14n2 + 55n + 21 = 0

Reorder the terms:
21 + 55n + 14n2 = 0

Solving
21 + 55n + 14n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(7 + 2n)' equal to zero and attempt to solve:

Simplifying
7 + 2n = 0

Solving
7 + 2n = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2n = 0 + -7
2n = 0 + -7

Combine like terms: 0 + -7 = -7
2n = -7

Divide each side by '2'.
n = -3.5

Simplifying
n = -3.5
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 = {-3.5, -0.4285714286}