-2(4n+10)+8n(n-7)=

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Solution for -2(4n+10)+8n(n-7)= equation: 


Simplifying
-2(4n + 10) + 8n(n + -7) = 0

Reorder the terms:
-2(10 + 4n) + 8n(n + -7) = 0
(10 * -2 + 4n * -2) + 8n(n + -7) = 0
(-20 + -8n) + 8n(n + -7) = 0

Reorder the terms:
-20 + -8n + 8n(-7 + n) = 0
-20 + -8n + (-7 * 8n + n * 8n) = 0
-20 + -8n + (-56n + 8n2) = 0

Combine like terms: -8n + -56n = -64n
-20 + -64n + 8n2 = 0

Solving
-20 + -64n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -16n + 2n2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + -16n + 2n2)' equal to zero and attempt to solve:

Simplifying
-5 + -16n + 2n2 = 0

Solving
-5 + -16n + 2n2 = 0

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

Divide each side by '2'.
-2.5 + -8n + n2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -8n + 2.5 + n2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -8n + n2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -8n + n2 = 0 + 2.5
-8n + n2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-8n + n2 = 2.5

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 = 2.5 + 16

Reorder the terms:
16 + -8n + n2 = 2.5 + 16

Combine like terms: 2.5 + 16 = 18.5
16 + -8n + n2 = 18.5

Factor a perfect square on the left side:
(n + -4)(n + -4) = 18.5

Calculate the square root of the right side: 4.301162634

Break this problem into two subproblems by setting 
(n + -4) equal to 4.301162634 and -4.301162634.


Subproblem 1
n + -4 = 4.301162634

Simplifying
n + -4 = 4.301162634

Reorder the terms:
-4 + n = 4.301162634

Solving
-4 + n = 4.301162634

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 = 4.301162634 + 4

Combine like terms: -4 + 4 = 0
0 + n = 4.301162634 + 4
n = 4.301162634 + 4

Combine like terms: 4.301162634 + 4 = 8.301162634
n = 8.301162634

Simplifying
n = 8.301162634


Subproblem 2
n + -4 = -4.301162634

Simplifying
n + -4 = -4.301162634

Reorder the terms:
-4 + n = -4.301162634

Solving
-4 + n = -4.301162634

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 = -4.301162634 + 4

Combine like terms: -4 + 4 = 0
0 + n = -4.301162634 + 4
n = -4.301162634 + 4

Combine like terms: -4.301162634 + 4 = -0.301162634
n = -0.301162634

Simplifying
n = -0.301162634


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {8.301162634, -0.301162634}
Solution
n = {8.301162634, -0.301162634}

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