n^2+10n-58=-2

Solution for n^2+10n-58=-2 equation:

Simplifying
n2 + 10n + -58 = -2

Reorder the terms:
-58 + 10n + n2 = -2

Solving
-58 + 10n + n2 = -2

Solving for variable 'n'.

Reorder the terms:
-58 + 2 + 10n + n2 = -2 + 2

Combine like terms: -58 + 2 = -56
-56 + 10n + n2 = -2 + 2

Combine like terms: -2 + 2 = 0
-56 + 10n + n2 = 0

Factor a trinomial.
(-14 + -1n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-14 + -1n)' equal to zero and attempt to solve:

Simplifying
-14 + -1n = 0

Solving
-14 + -1n = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1n = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1n = 0 + 14
-1n = 0 + 14

Combine like terms: 0 + 14 = 14
-1n = 14

Divide each side by '-1'.
n = -14

Simplifying
n = -14
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 = {-14, 4}