-0.25n^2+6n-27=0

Solution for -0.25n^2+6n-27=0 equation:

Simplifying
-0.25n2 + 6n + -27 = 0

Reorder the terms:
-27 + 6n + -0.25n2 = 0

Solving
-27 + 6n + -0.25n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
108 + -24n + n2 = 0

Move the constant term to the right:

Add '-108' to each side of the equation.
108 + -24n + -108 + n2 = 0 + -108

Reorder the terms:
108 + -108 + -24n + n2 = 0 + -108

Combine like terms: 108 + -108 = 0
0 + -24n + n2 = 0 + -108
-24n + n2 = 0 + -108

Combine like terms: 0 + -108 = -108
-24n + n2 = -108

The n term is -24n.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24n + 144 + n2 = -108 + 144

Reorder the terms:
144 + -24n + n2 = -108 + 144

Combine like terms: -108 + 144 = 36
144 + -24n + n2 = 36

Factor a perfect square on the left side:
(n + -12)(n + -12) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(n + -12) equal to 6 and -6.

Subproblem 1
n + -12 = 6

Simplifying
n + -12 = 6

Reorder the terms:
-12 + n = 6

Solving
-12 + n = 6

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '12' to each side of the equation.
-12 + 12 + n = 6 + 12

Combine like terms: -12 + 12 = 0
0 + n = 6 + 12
n = 6 + 12

Combine like terms: 6 + 12 = 18
n = 18

Simplifying
n = 18

Subproblem 2
n + -12 = -6

Simplifying
n + -12 = -6

Reorder the terms:
-12 + n = -6

Solving
-12 + n = -6

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '12' to each side of the equation.
-12 + 12 + n = -6 + 12

Combine like terms: -12 + 12 = 0
0 + n = -6 + 12
n = -6 + 12

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

Simplifying
n = 6

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {18, 6}