2n^2-4n-19=-3

Solution for 2n^2-4n-19=-3 equation:

Simplifying
2n2 + -4n + -19 = -3

Reorder the terms:
-19 + -4n + 2n2 = -3

Solving
-19 + -4n + 2n2 = -3

Solving for variable 'n'.

Reorder the terms:
-19 + 3 + -4n + 2n2 = -3 + 3

Combine like terms: -19 + 3 = -16
-16 + -4n + 2n2 = -3 + 3

Combine like terms: -3 + 3 = 0
-16 + -4n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2n + n2) = 0

Factor a trinomial.
2((-2 + -1n)(4 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 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 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2
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 = {-2, 4}