36-2(n-4)n=10

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Solution for 36-2(n-4)n=10 equation: 


Simplifying
36 + -2(n + -4) * n = 10

Reorder the terms:
36 + -2(-4 + n) * n = 10

Reorder the terms for easier multiplication:
36 + -2n(-4 + n) = 10
36 + (-4 * -2n + n * -2n) = 10
36 + (8n + -2n2) = 10

Solving
36 + 8n + -2n2 = 10

Solving for variable 'n'.

Reorder the terms:
36 + -10 + 8n + -2n2 = 10 + -10

Combine like terms: 36 + -10 = 26
26 + 8n + -2n2 = 10 + -10

Combine like terms: 10 + -10 = 0
26 + 8n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + 4n + -1n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(13 + 4n + -1n2)' equal to zero and attempt to solve:

Simplifying
13 + 4n + -1n2 = 0

Solving
13 + 4n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-13 + -4n + n2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -4n + 13 + n2 = 0 + 13

Reorder the terms:
-13 + 13 + -4n + n2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -4n + n2 = 0 + 13
-4n + n2 = 0 + 13

Combine like terms: 0 + 13 = 13
-4n + n2 = 13

The n term is -4n.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4n + 4 + n2 = 13 + 4

Reorder the terms:
4 + -4n + n2 = 13 + 4

Combine like terms: 13 + 4 = 17
4 + -4n + n2 = 17

Factor a perfect square on the left side:
(n + -2)(n + -2) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(n + -2) equal to 4.123105626 and -4.123105626.


Subproblem 1
n + -2 = 4.123105626

Simplifying
n + -2 = 4.123105626

Reorder the terms:
-2 + n = 4.123105626

Solving
-2 + n = 4.123105626

Solving for variable 'n'.

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

Add '2' to each side of the equation.
-2 + 2 + n = 4.123105626 + 2

Combine like terms: -2 + 2 = 0
0 + n = 4.123105626 + 2
n = 4.123105626 + 2

Combine like terms: 4.123105626 + 2 = 6.123105626
n = 6.123105626

Simplifying
n = 6.123105626


Subproblem 2
n + -2 = -4.123105626

Simplifying
n + -2 = -4.123105626

Reorder the terms:
-2 + n = -4.123105626

Solving
-2 + n = -4.123105626

Solving for variable 'n'.

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

Add '2' to each side of the equation.
-2 + 2 + n = -4.123105626 + 2

Combine like terms: -2 + 2 = 0
0 + n = -4.123105626 + 2
n = -4.123105626 + 2

Combine like terms: -4.123105626 + 2 = -2.123105626
n = -2.123105626

Simplifying
n = -2.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.123105626, -2.123105626}
Solution
n = {6.123105626, -2.123105626}

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