n^2=3n-12+6

Solution for n^2=3n-12+6 equation:

Simplifying
n2 = 3n + -12 + 6

Reorder the terms:
n2 = -12 + 6 + 3n

Combine like terms: -12 + 6 = -6
n2 = -6 + 3n

Solving
n2 = -6 + 3n

Solving for variable 'n'.

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

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

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

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

Begin completing the square.

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.