-5n-4n(-7-4n)=36+7n

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Solution for -5n-4n(-7-4n)=36+7n equation: 


Simplifying
-5n + -4n(-7 + -4n) = 36 + 7n
-5n + (-7 * -4n + -4n * -4n) = 36 + 7n
-5n + (28n + 16n2) = 36 + 7n

Combine like terms: -5n + 28n = 23n
23n + 16n2 = 36 + 7n

Solving
23n + 16n2 = 36 + 7n

Solving for variable 'n'.

Reorder the terms:
-36 + 23n + -7n + 16n2 = 36 + 7n + -36 + -7n

Combine like terms: 23n + -7n = 16n
-36 + 16n + 16n2 = 36 + 7n + -36 + -7n

Reorder the terms:
-36 + 16n + 16n2 = 36 + -36 + 7n + -7n

Combine like terms: 36 + -36 = 0
-36 + 16n + 16n2 = 0 + 7n + -7n
-36 + 16n + 16n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
-36 + 16n + 16n2 = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-9 + 4n + 4n2)' equal to zero and attempt to solve:

Simplifying
-9 + 4n + 4n2 = 0

Solving
-9 + 4n + 4n2 = 0

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

Divide each side by '4'.
-2.25 + n + n2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + n + 2.25 + n2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + n + n2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + n + n2 = 0 + 2.25
n + n2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
n + n2 = 2.25

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + n2 = 2.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + n2 = 2.25 + 0.25

Combine like terms: 2.25 + 0.25 = 2.5
1.25 + n2 = 2.5

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(n + 0.5) equal to 1.58113883 and -1.58113883.


Subproblem 1
n + 0.5 = 1.58113883

Simplifying
n + 0.5 = 1.58113883

Reorder the terms:
0.5 + n = 1.58113883

Solving
0.5 + n = 1.58113883

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = 1.58113883 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 1.58113883 + -0.5
n = 1.58113883 + -0.5

Combine like terms: 1.58113883 + -0.5 = 1.08113883
n = 1.08113883

Simplifying
n = 1.08113883


Subproblem 2
n + 0.5 = -1.58113883

Simplifying
n + 0.5 = -1.58113883

Reorder the terms:
0.5 + n = -1.58113883

Solving
0.5 + n = -1.58113883

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = -1.58113883 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -1.58113883 + -0.5
n = -1.58113883 + -0.5

Combine like terms: -1.58113883 + -0.5 = -2.08113883
n = -2.08113883

Simplifying
n = -2.08113883


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.08113883, -2.08113883}
Solution
n = {1.08113883, -2.08113883}

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