n-12=n^2-6n+27

Solution for n-12=n^2-6n+27 equation:

Simplifying
n + -12 = n2 + -6n + 27

Reorder the terms:
-12 + n = n2 + -6n + 27

Reorder the terms:
-12 + n = 27 + -6n + n2

Solving
-12 + n = 27 + -6n + n2

Solving for variable 'n'.

Reorder the terms:
-12 + -27 + n + 6n + -1n2 = 27 + -6n + n2 + -27 + 6n + -1n2

Combine like terms: -12 + -27 = -39
-39 + n + 6n + -1n2 = 27 + -6n + n2 + -27 + 6n + -1n2

Combine like terms: n + 6n = 7n
-39 + 7n + -1n2 = 27 + -6n + n2 + -27 + 6n + -1n2

Reorder the terms:
-39 + 7n + -1n2 = 27 + -27 + -6n + 6n + n2 + -1n2

Combine like terms: 27 + -27 = 0
-39 + 7n + -1n2 = 0 + -6n + 6n + n2 + -1n2
-39 + 7n + -1n2 = -6n + 6n + n2 + -1n2

Combine like terms: -6n + 6n = 0
-39 + 7n + -1n2 = 0 + n2 + -1n2
-39 + 7n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-39 + 7n + -1n2 = 0

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

Divide each side by '-1'.
39 + -7n + n2 = 0

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + -7n + -39 + n2 = 0 + -39

Reorder the terms:
39 + -39 + -7n + n2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -7n + n2 = 0 + -39
-7n + n2 = 0 + -39

Combine like terms: 0 + -39 = -39
-7n + n2 = -39

The n term is -7n.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7n + 12.25 + n2 = -39 + 12.25

Reorder the terms:
12.25 + -7n + n2 = -39 + 12.25

Combine like terms: -39 + 12.25 = -26.75
12.25 + -7n + n2 = -26.75

Factor a perfect square on the left side:
(n + -3.5)(n + -3.5) = -26.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.