n^2+2n-19=5

Solution for n^2+2n-19=5 equation:

Simplifying
n2 + 2n + -19 = 5

Reorder the terms:
-19 + 2n + n2 = 5

Solving
-19 + 2n + n2 = 5

Solving for variable 'n'.

Reorder the terms:
-19 + -5 + 2n + n2 = 5 + -5

Combine like terms: -19 + -5 = -24
-24 + 2n + n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-24 + 2n + n2 = 0

Factor a trinomial.
(-6 + -1n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 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 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-6, 4}