4n^2+36n+28=0

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Solution for 4n^2+36n+28=0 equation: 


Simplifying
4n2 + 36n + 28 = 0

Reorder the terms:
28 + 36n + 4n2 = 0

Solving
28 + 36n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + 9n + n2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7 + 9n + n2)' equal to zero and attempt to solve:

Simplifying
7 + 9n + n2 = 0

Solving
7 + 9n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 9n + -7 + n2 = 0 + -7

Reorder the terms:
7 + -7 + 9n + n2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 9n + n2 = 0 + -7
9n + n2 = 0 + -7

Combine like terms: 0 + -7 = -7
9n + n2 = -7

The n term is 9n.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9n + 20.25 + n2 = -7 + 20.25

Reorder the terms:
20.25 + 9n + n2 = -7 + 20.25

Combine like terms: -7 + 20.25 = 13.25
20.25 + 9n + n2 = 13.25

Factor a perfect square on the left side:
(n + 4.5)(n + 4.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(n + 4.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
n + 4.5 = 3.640054945

Simplifying
n + 4.5 = 3.640054945

Reorder the terms:
4.5 + n = 3.640054945

Solving
4.5 + n = 3.640054945

Solving for variable 'n'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + n = 3.640054945 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + n = 3.640054945 + -4.5
n = 3.640054945 + -4.5

Combine like terms: 3.640054945 + -4.5 = -0.859945055
n = -0.859945055

Simplifying
n = -0.859945055


Subproblem 2
n + 4.5 = -3.640054945

Simplifying
n + 4.5 = -3.640054945

Reorder the terms:
4.5 + n = -3.640054945

Solving
4.5 + n = -3.640054945

Solving for variable 'n'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + n = -3.640054945 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + n = -3.640054945 + -4.5
n = -3.640054945 + -4.5

Combine like terms: -3.640054945 + -4.5 = -8.140054945
n = -8.140054945

Simplifying
n = -8.140054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.859945055, -8.140054945}
Solution
n = {-0.859945055, -8.140054945}

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