-(n+8)n=-8n+2(4n-4)

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Solution for -(n+8)n=-8n+2(4n-4) equation:


Simplifying
-1(n + 8) * n = -8n + 2(4n + -4)

Reorder the terms:
-1(8 + n) * n = -8n + 2(4n + -4)

Reorder the terms for easier multiplication:
-1n(8 + n) = -8n + 2(4n + -4)
(8 * -1n + n * -1n) = -8n + 2(4n + -4)
(-8n + -1n2) = -8n + 2(4n + -4)

Reorder the terms:
-8n + -1n2 = -8n + 2(-4 + 4n)
-8n + -1n2 = -8n + (-4 * 2 + 4n * 2)
-8n + -1n2 = -8n + (-8 + 8n)

Reorder the terms:
-8n + -1n2 = -8 + -8n + 8n

Combine like terms: -8n + 8n = 0
-8n + -1n2 = -8 + 0
-8n + -1n2 = -8

Solving
-8n + -1n2 = -8

Solving for variable 'n'.

Reorder the terms:
8 + -8n + -1n2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + -8n + -1n2 = 0

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

Divide each side by '-1'.
-8 + 8n + n2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 8n + 8 + n2 = 0 + 8

Reorder the terms:
-8 + 8 + 8n + n2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 8n + n2 = 0 + 8
8n + n2 = 0 + 8

Combine like terms: 0 + 8 = 8
8n + n2 = 8

The n term is 8n.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8n + 16 + n2 = 8 + 16

Reorder the terms:
16 + 8n + n2 = 8 + 16

Combine like terms: 8 + 16 = 24
16 + 8n + n2 = 24

Factor a perfect square on the left side:
(n + 4)(n + 4) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(n + 4) equal to 4.898979486 and -4.898979486.

Subproblem 1

n + 4 = 4.898979486 Simplifying n + 4 = 4.898979486 Reorder the terms: 4 + n = 4.898979486 Solving 4 + n = 4.898979486 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + n = 4.898979486 + -4 n = 4.898979486 + -4 Combine like terms: 4.898979486 + -4 = 0.898979486 n = 0.898979486 Simplifying n = 0.898979486

Subproblem 2

n + 4 = -4.898979486 Simplifying n + 4 = -4.898979486 Reorder the terms: 4 + n = -4.898979486 Solving 4 + n = -4.898979486 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = -4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + n = -4.898979486 + -4 n = -4.898979486 + -4 Combine like terms: -4.898979486 + -4 = -8.898979486 n = -8.898979486 Simplifying n = -8.898979486

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.898979486, -8.898979486}

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