10n^2+39n+14=0

Solution for 10n^2+39n+14=0 equation:

Simplifying
10n2 + 39n + 14 = 0

Reorder the terms:
14 + 39n + 10n2 = 0

Solving
14 + 39n + 10n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(7 + 2n)(2 + 5n) = 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 '(2 + 5n)' equal to zero and attempt to solve:

Simplifying
2 + 5n = 0

Solving
2 + 5n = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5n = 0 + -2
5n = 0 + -2

Combine like terms: 0 + -2 = -2
5n = -2

Divide each side by '5'.
n = -0.4

Simplifying
n = -0.4
Solution
n = {-3.5, -0.4}