5n^2+23n+26=0

Solution for 5n^2+23n+26=0 equation:

Simplifying
5n2 + 23n + 26 = 0

Reorder the terms:
26 + 23n + 5n2 = 0

Solving
26 + 23n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(13 + 5n)(2 + n) = 0

Subproblem 1
Set the factor '(13 + 5n)' equal to zero and attempt to solve:

Simplifying
13 + 5n = 0

Solving
13 + 5n = 0

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

Add '-13' to each side of the equation.
13 + -13 + 5n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 5n = 0 + -13
5n = 0 + -13

Combine like terms: 0 + -13 = -13
5n = -13

Divide each side by '5'.
n = -2.6

Simplifying
n = -2.6
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

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

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

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

Simplifying
n = -2
Solution
n = {-2.6, -2}