n^2+5=-3+6n

Solution for n^2+5=-3+6n equation:

Simplifying
n2 + 5 = -3 + 6n

Reorder the terms:
5 + n2 = -3 + 6n

Solving
5 + n2 = -3 + 6n

Solving for variable 'n'.

Reorder the terms:
5 + 3 + -6n + n2 = -3 + 6n + 3 + -6n

Combine like terms: 5 + 3 = 8
8 + -6n + n2 = -3 + 6n + 3 + -6n

Reorder the terms:
8 + -6n + n2 = -3 + 3 + 6n + -6n

Combine like terms: -3 + 3 = 0
8 + -6n + n2 = 0 + 6n + -6n
8 + -6n + n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
8 + -6n + n2 = 0

Factor a trinomial.
(2 + -1n)(4 + -1n) = 0

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
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 = {2, 4}