n^2+19n-68=-2

Solution for n^2+19n-68=-2 equation:

Simplifying
n2 + 19n + -68 = -2

Reorder the terms:
-68 + 19n + n2 = -2

Solving
-68 + 19n + n2 = -2

Solving for variable 'n'.

Reorder the terms:
-68 + 2 + 19n + n2 = -2 + 2

Combine like terms: -68 + 2 = -66
-66 + 19n + n2 = -2 + 2

Combine like terms: -2 + 2 = 0
-66 + 19n + n2 = 0

Factor a trinomial.
(-22 + -1n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-22 + -1n)' equal to zero and attempt to solve:

Simplifying
-22 + -1n = 0

Solving
-22 + -1n = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1n = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1n = 0 + 22
-1n = 0 + 22

Combine like terms: 0 + 22 = 22
-1n = 22

Divide each side by '-1'.
n = -22

Simplifying
n = -22
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 = {-22, 3}