n^2-3n-12=0

Solution for n^2-3n-12=0 equation:

Simplifying
n2 + -3n + -12 = 0

Reorder the terms:
-12 + -3n + n2 = 0

Solving
-12 + -3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -3n + 12 + n2 = 0 + 12

Reorder the terms:
-12 + 12 + -3n + n2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -3n + n2 = 0 + 12
-3n + n2 = 0 + 12

Combine like terms: 0 + 12 = 12
-3n + n2 = 12

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 = 12 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + -3n + n2 = 14.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(n + -1.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
n + -1.5 = 3.774917218

Simplifying
n + -1.5 = 3.774917218

Reorder the terms:
-1.5 + n = 3.774917218

Solving
-1.5 + n = 3.774917218

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 3.774917218 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 3.774917218 + 1.5
n = 3.774917218 + 1.5

Combine like terms: 3.774917218 + 1.5 = 5.274917218
n = 5.274917218

Simplifying
n = 5.274917218

Subproblem 2
n + -1.5 = -3.774917218

Simplifying
n + -1.5 = -3.774917218

Reorder the terms:
-1.5 + n = -3.774917218

Solving
-1.5 + n = -3.774917218

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -3.774917218 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -3.774917218 + 1.5
n = -3.774917218 + 1.5

Combine like terms: -3.774917218 + 1.5 = -2.274917218
n = -2.274917218

Simplifying
n = -2.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.274917218, -2.274917218}