3n^2+12n+8=0

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Solution for 3n^2+12n+8=0 equation: 


Simplifying
3n2 + 12n + 8 = 0

Reorder the terms:
8 + 12n + 3n2 = 0

Solving
8 + 12n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
2.666666667 + 4n + n2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 4n + -2.666666667 + n2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 4n + n2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 4n + n2 = 0 + -2.666666667
4n + n2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
4n + n2 = -2.666666667

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 = -2.666666667 + 4

Reorder the terms:
4 + 4n + n2 = -2.666666667 + 4

Combine like terms: -2.666666667 + 4 = 1.333333333
4 + 4n + n2 = 1.333333333

Factor a perfect square on the left side:
(n + 2)(n + 2) = 1.333333333

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(n + 2) equal to 1.154700538 and -1.154700538.


Subproblem 1
n + 2 = 1.154700538

Simplifying
n + 2 = 1.154700538

Reorder the terms:
2 + n = 1.154700538

Solving
2 + n = 1.154700538

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 = 1.154700538 + -2

Combine like terms: 2 + -2 = 0
0 + n = 1.154700538 + -2
n = 1.154700538 + -2

Combine like terms: 1.154700538 + -2 = -0.845299462
n = -0.845299462

Simplifying
n = -0.845299462


Subproblem 2
n + 2 = -1.154700538

Simplifying
n + 2 = -1.154700538

Reorder the terms:
2 + n = -1.154700538

Solving
2 + n = -1.154700538

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 = -1.154700538 + -2

Combine like terms: 2 + -2 = 0
0 + n = -1.154700538 + -2
n = -1.154700538 + -2

Combine like terms: -1.154700538 + -2 = -3.154700538
n = -3.154700538

Simplifying
n = -3.154700538


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.845299462, -3.154700538}

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