3n^2-28n+12=0

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Solution for 3n^2-28n+12=0 equation: 


Simplifying
3n2 + -28n + 12 = 0

Reorder the terms:
12 + -28n + 3n2 = 0

Solving
12 + -28n + 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'.
4 + -9.333333333n + n2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -9.333333333n + -4 + n2 = 0 + -4

Reorder the terms:
4 + -4 + -9.333333333n + n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9.333333333n + n2 = 0 + -4
-9.333333333n + n2 = 0 + -4

Combine like terms: 0 + -4 = -4
-9.333333333n + n2 = -4

The n term is -9.333333333n.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333n + 21.77777778 + n2 = -4 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333n + n2 = -4 + 21.77777778

Combine like terms: -4 + 21.77777778 = 17.77777778
21.77777778 + -9.333333333n + n2 = 17.77777778

Factor a perfect square on the left side:
(n + -4.666666667)(n + -4.666666667) = 17.77777778

Calculate the square root of the right side: 4.216370214

Break this problem into two subproblems by setting 
(n + -4.666666667) equal to 4.216370214 and -4.216370214.


Subproblem 1
n + -4.666666667 = 4.216370214

Simplifying
n + -4.666666667 = 4.216370214

Reorder the terms:
-4.666666667 + n = 4.216370214

Solving
-4.666666667 + n = 4.216370214

Solving for variable 'n'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + n = 4.216370214 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + n = 4.216370214 + 4.666666667
n = 4.216370214 + 4.666666667

Combine like terms: 4.216370214 + 4.666666667 = 8.883036881
n = 8.883036881

Simplifying
n = 8.883036881


Subproblem 2
n + -4.666666667 = -4.216370214

Simplifying
n + -4.666666667 = -4.216370214

Reorder the terms:
-4.666666667 + n = -4.216370214

Solving
-4.666666667 + n = -4.216370214

Solving for variable 'n'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + n = -4.216370214 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + n = -4.216370214 + 4.666666667
n = -4.216370214 + 4.666666667

Combine like terms: -4.216370214 + 4.666666667 = 0.450296453
n = 0.450296453

Simplifying
n = 0.450296453


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {8.883036881, 0.450296453}

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