n^2+20n+49=-2

Solution for n^2+20n+49=-2 equation:

Simplifying
n2 + 20n + 49 = -2

Reorder the terms:
49 + 20n + n2 = -2

Solving
49 + 20n + n2 = -2

Solving for variable 'n'.

Reorder the terms:
49 + 2 + 20n + n2 = -2 + 2

Combine like terms: 49 + 2 = 51
51 + 20n + n2 = -2 + 2

Combine like terms: -2 + 2 = 0
51 + 20n + n2 = 0

Factor a trinomial.
(17 + n)(3 + n) = 0

Subproblem 1
Set the factor '(17 + n)' equal to zero and attempt to solve:

Simplifying
17 + n = 0

Solving
17 + n = 0

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

Add '-17' to each side of the equation.
17 + -17 + n = 0 + -17

Combine like terms: 17 + -17 = 0
0 + n = 0 + -17
n = 0 + -17

Combine like terms: 0 + -17 = -17
n = -17

Simplifying
n = -17
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

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

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

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

Simplifying
n = -3
Solution
n = {-17, -3}