n^2+7n+23=-5n+3

Solution for n^2+7n+23=-5n+3 equation:

Simplifying
n2 + 7n + 23 = -5n + 3

Reorder the terms:
23 + 7n + n2 = -5n + 3

Reorder the terms:
23 + 7n + n2 = 3 + -5n

Solving
23 + 7n + n2 = 3 + -5n

Solving for variable 'n'.

Reorder the terms:
23 + -3 + 7n + 5n + n2 = 3 + -5n + -3 + 5n

Combine like terms: 23 + -3 = 20
20 + 7n + 5n + n2 = 3 + -5n + -3 + 5n

Combine like terms: 7n + 5n = 12n
20 + 12n + n2 = 3 + -5n + -3 + 5n

Reorder the terms:
20 + 12n + n2 = 3 + -3 + -5n + 5n

Combine like terms: 3 + -3 = 0
20 + 12n + n2 = 0 + -5n + 5n
20 + 12n + n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
20 + 12n + n2 = 0

Factor a trinomial.
(10 + n)(2 + n) = 0

Subproblem 1
Set the factor '(10 + n)' equal to zero and attempt to solve:

Simplifying
10 + n = 0

Solving
10 + n = 0

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

Add '-10' to each side of the equation.
10 + -10 + n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + n = 0 + -10
n = 0 + -10

Combine like terms: 0 + -10 = -10
n = -10

Simplifying
n = -10
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

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

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

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

Simplifying
n = -2
Solution
n = {-10, -2}