2n^2+13n=-20

Solution for 2n^2+13n=-20 equation:

Simplifying
2n2 + 13n = -20

Reorder the terms:
13n + 2n2 = -20

Solving
13n + 2n2 = -20

Solving for variable 'n'.

Reorder the terms:
20 + 13n + 2n2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + 13n + 2n2 = 0

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

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 '(5 + 2n)' equal to zero and attempt to solve:

Simplifying
5 + 2n = 0

Solving
5 + 2n = 0

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

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

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

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

Divide each side by '2'.
n = -2.5

Simplifying
n = -2.5
Solution
n = {-4, -2.5}