n^2-4n-12=30

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Solution for n^2-4n-12=30 equation: 


Simplifying
n2 + -4n + -12 = 30

Reorder the terms:
-12 + -4n + n2 = 30

Solving
-12 + -4n + n2 = 30

Solving for variable 'n'.

Reorder the terms:
-12 + -30 + -4n + n2 = 30 + -30

Combine like terms: -12 + -30 = -42
-42 + -4n + n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-42 + -4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + -4n + 42 + n2 = 0 + 42

Reorder the terms:
-42 + 42 + -4n + n2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -4n + n2 = 0 + 42
-4n + n2 = 0 + 42

Combine like terms: 0 + 42 = 42
-4n + n2 = 42

The n term is -4n.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4n + 4 + n2 = 42 + 4

Reorder the terms:
4 + -4n + n2 = 42 + 4

Combine like terms: 42 + 4 = 46
4 + -4n + n2 = 46

Factor a perfect square on the left side:
(n + -2)(n + -2) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(n + -2) equal to 6.782329983 and -6.782329983.


Subproblem 1
n + -2 = 6.782329983

Simplifying
n + -2 = 6.782329983

Reorder the terms:
-2 + n = 6.782329983

Solving
-2 + n = 6.782329983

Solving for variable 'n'.

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

Add '2' to each side of the equation.
-2 + 2 + n = 6.782329983 + 2

Combine like terms: -2 + 2 = 0
0 + n = 6.782329983 + 2
n = 6.782329983 + 2

Combine like terms: 6.782329983 + 2 = 8.782329983
n = 8.782329983

Simplifying
n = 8.782329983


Subproblem 2
n + -2 = -6.782329983

Simplifying
n + -2 = -6.782329983

Reorder the terms:
-2 + n = -6.782329983

Solving
-2 + n = -6.782329983

Solving for variable 'n'.

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

Add '2' to each side of the equation.
-2 + 2 + n = -6.782329983 + 2

Combine like terms: -2 + 2 = 0
0 + n = -6.782329983 + 2
n = -6.782329983 + 2

Combine like terms: -6.782329983 + 2 = -4.782329983
n = -4.782329983

Simplifying
n = -4.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {8.782329983, -4.782329983}

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