2n^2+20n+40=-2

Solution for 2n^2+20n+40=-2 equation:

Simplifying
2n2 + 20n + 40 = -2

Reorder the terms:
40 + 20n + 2n2 = -2

Solving
40 + 20n + 2n2 = -2

Solving for variable 'n'.

Reorder the terms:
40 + 2 + 20n + 2n2 = -2 + 2

Combine like terms: 40 + 2 = 42
42 + 20n + 2n2 = -2 + 2

Combine like terms: -2 + 2 = 0
42 + 20n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 10n + n2) = 0

Factor a trinomial.
2((7 + n)(3 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 0

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

Add '-7' to each side of the equation.
7 + -7 + n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + n = 0 + -7
n = 0 + -7

Combine like terms: 0 + -7 = -7
n = -7

Simplifying
n = -7
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 = {-7, -3}