-3n^2+14n+36=0

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Solution for -3n^2+14n+36=0 equation: 


Simplifying
-3n2 + 14n + 36 = 0

Reorder the terms:
36 + 14n + -3n2 = 0

Solving
36 + 14n + -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'.
-12 + -4.666666667n + n2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -4.666666667n + 12 + n2 = 0 + 12

Reorder the terms:
-12 + 12 + -4.666666667n + n2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -4.666666667n + n2 = 0 + 12
-4.666666667n + n2 = 0 + 12

Combine like terms: 0 + 12 = 12
-4.666666667n + n2 = 12

The n term is -4.666666667n.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667n + 5.444444448 + n2 = 12 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667n + n2 = 12 + 5.444444448

Combine like terms: 12 + 5.444444448 = 17.444444448
5.444444448 + -4.666666667n + n2 = 17.444444448

Factor a perfect square on the left side:
(n + -2.333333334)(n + -2.333333334) = 17.444444448

Calculate the square root of the right side: 4.176654696

Break this problem into two subproblems by setting 
(n + -2.333333334) equal to 4.176654696 and -4.176654696.


Subproblem 1
n + -2.333333334 = 4.176654696

Simplifying
n + -2.333333334 = 4.176654696

Reorder the terms:
-2.333333334 + n = 4.176654696

Solving
-2.333333334 + n = 4.176654696

Solving for variable 'n'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + n = 4.176654696 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + n = 4.176654696 + 2.333333334
n = 4.176654696 + 2.333333334

Combine like terms: 4.176654696 + 2.333333334 = 6.50998803
n = 6.50998803

Simplifying
n = 6.50998803


Subproblem 2
n + -2.333333334 = -4.176654696

Simplifying
n + -2.333333334 = -4.176654696

Reorder the terms:
-2.333333334 + n = -4.176654696

Solving
-2.333333334 + n = -4.176654696

Solving for variable 'n'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + n = -4.176654696 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + n = -4.176654696 + 2.333333334
n = -4.176654696 + 2.333333334

Combine like terms: -4.176654696 + 2.333333334 = -1.843321362
n = -1.843321362

Simplifying
n = -1.843321362


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.50998803, -1.843321362}

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