3n+10=n^2+16

Solution for 3n+10=n^2+16 equation:

Simplifying
3n + 10 = n2 + 16

Reorder the terms:
10 + 3n = n2 + 16

Reorder the terms:
10 + 3n = 16 + n2

Solving
10 + 3n = 16 + n2

Solving for variable 'n'.

Reorder the terms:
10 + -16 + 3n + -1n2 = 16 + n2 + -16 + -1n2

Combine like terms: 10 + -16 = -6
-6 + 3n + -1n2 = 16 + n2 + -16 + -1n2

Reorder the terms:
-6 + 3n + -1n2 = 16 + -16 + n2 + -1n2

Combine like terms: 16 + -16 = 0
-6 + 3n + -1n2 = 0 + n2 + -1n2
-6 + 3n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-6 + 3n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -3n + n2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -3n + -6 + n2 = 0 + -6

Reorder the terms:
6 + -6 + -3n + n2 = 0 + -6

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

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

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = -6 + 2.25

Reorder the terms:
2.25 + -3n + n2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + -3n + n2 = -3.75

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.