n^2+6n-46=-6

Solution for n^2+6n-46=-6 equation:

Simplifying
n2 + 6n + -46 = -6

Reorder the terms:
-46 + 6n + n2 = -6

Solving
-46 + 6n + n2 = -6

Solving for variable 'n'.

Reorder the terms:
-46 + 6 + 6n + n2 = -6 + 6

Combine like terms: -46 + 6 = -40
-40 + 6n + n2 = -6 + 6

Combine like terms: -6 + 6 = 0
-40 + 6n + n2 = 0

Factor a trinomial.
(-10 + -1n)(4 + -1n) = 0

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

Simplifying
-10 + -1n = 0

Solving
-10 + -1n = 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 + -1n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n = 0 + 10
-1n = 0 + 10

Combine like terms: 0 + 10 = 10
-1n = 10

Divide each side by '-1'.
n = -10

Simplifying
n = -10
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 = {-10, 4}