2n^2+13n+19=4

Solution for 2n^2+13n+19=4 equation:

Simplifying
2n2 + 13n + 19 = 4

Reorder the terms:
19 + 13n + 2n2 = 4

Solving
19 + 13n + 2n2 = 4

Solving for variable 'n'.

Reorder the terms:
19 + -4 + 13n + 2n2 = 4 + -4

Combine like terms: 19 + -4 = 15
15 + 13n + 2n2 = 4 + -4

Combine like terms: 4 + -4 = 0
15 + 13n + 2n2 = 0

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

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

Simplifying
5 + n = 0

Solving
5 + n = 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 + n = 0 + -5

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

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

Simplifying
n = -5
Subproblem 2
Set the factor '(3 + 2n)' equal to zero and attempt to solve:

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Solution
n = {-5, -1.5}