3n^2-16n+12=0

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Solution for 3n^2-16n+12=0 equation: 


Simplifying
3n2 + -16n + 12 = 0

Reorder the terms:
12 + -16n + 3n2 = 0

Solving
12 + -16n + 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 + -5.333333333n + n2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -5.333333333n + -4 + n2 = 0 + -4

Reorder the terms:
4 + -4 + -5.333333333n + n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5.333333333n + n2 = 0 + -4
-5.333333333n + n2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5.333333333n + n2 = -4

The n term is -5.333333333n.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333n + 7.111111113 + n2 = -4 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333n + n2 = -4 + 7.111111113

Combine like terms: -4 + 7.111111113 = 3.111111113
7.111111113 + -5.333333333n + n2 = 3.111111113

Factor a perfect square on the left side:
(n + -2.666666667)(n + -2.666666667) = 3.111111113

Calculate the square root of the right side: 1.763834208

Break this problem into two subproblems by setting 
(n + -2.666666667) equal to 1.763834208 and -1.763834208.


Subproblem 1
n + -2.666666667 = 1.763834208

Simplifying
n + -2.666666667 = 1.763834208

Reorder the terms:
-2.666666667 + n = 1.763834208

Solving
-2.666666667 + n = 1.763834208

Solving for variable 'n'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + n = 1.763834208 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + n = 1.763834208 + 2.666666667
n = 1.763834208 + 2.666666667

Combine like terms: 1.763834208 + 2.666666667 = 4.430500875
n = 4.430500875

Simplifying
n = 4.430500875


Subproblem 2
n + -2.666666667 = -1.763834208

Simplifying
n + -2.666666667 = -1.763834208

Reorder the terms:
-2.666666667 + n = -1.763834208

Solving
-2.666666667 + n = -1.763834208

Solving for variable 'n'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + n = -1.763834208 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + n = -1.763834208 + 2.666666667
n = -1.763834208 + 2.666666667

Combine like terms: -1.763834208 + 2.666666667 = 0.902832459
n = 0.902832459

Simplifying
n = 0.902832459


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.430500875, 0.902832459}

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