n^2+2n-19=-4

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

Simplifying
n2 + 2n + -19 = -4

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

Solving
-19 + 2n + n2 = -4

Solving for variable 'n'.

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

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

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

Factor a trinomial.
(-5 + -1n)(3 + -1n) = 0

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

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 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 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-5, 3}