-5(7n-8)-7n(n-4)=

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Solution for -5(7n-8)-7n(n-4)= equation: 


Simplifying
-5(7n + -8) + -7n(n + -4) = 0

Reorder the terms:
-5(-8 + 7n) + -7n(n + -4) = 0
(-8 * -5 + 7n * -5) + -7n(n + -4) = 0
(40 + -35n) + -7n(n + -4) = 0

Reorder the terms:
40 + -35n + -7n(-4 + n) = 0
40 + -35n + (-4 * -7n + n * -7n) = 0
40 + -35n + (28n + -7n2) = 0

Combine like terms: -35n + 28n = -7n
40 + -7n + -7n2 = 0

Solving
40 + -7n + -7n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-5.714285714 + n + n2 = 0

Move the constant term to the right:

Add '5.714285714' to each side of the equation.
-5.714285714 + n + 5.714285714 + n2 = 0 + 5.714285714

Reorder the terms:
-5.714285714 + 5.714285714 + n + n2 = 0 + 5.714285714

Combine like terms: -5.714285714 + 5.714285714 = 0.000000000
0.000000000 + n + n2 = 0 + 5.714285714
n + n2 = 0 + 5.714285714

Combine like terms: 0 + 5.714285714 = 5.714285714
n + n2 = 5.714285714

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 = 5.714285714 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + n2 = 5.714285714 + 0.25

Combine like terms: 5.714285714 + 0.25 = 5.964285714
1.25 + n2 = 5.964285714

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 5.964285714

Calculate the square root of the right side: 2.442188714

Break this problem into two subproblems by setting 
(n + 0.5) equal to 2.442188714 and -2.442188714.


Subproblem 1
n + 0.5 = 2.442188714

Simplifying
n + 0.5 = 2.442188714

Reorder the terms:
0.5 + n = 2.442188714

Solving
0.5 + n = 2.442188714

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 = 2.442188714 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 2.442188714 + -0.5
n = 2.442188714 + -0.5

Combine like terms: 2.442188714 + -0.5 = 1.942188714
n = 1.942188714

Simplifying
n = 1.942188714


Subproblem 2
n + 0.5 = -2.442188714

Simplifying
n + 0.5 = -2.442188714

Reorder the terms:
0.5 + n = -2.442188714

Solving
0.5 + n = -2.442188714

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 = -2.442188714 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -2.442188714 + -0.5
n = -2.442188714 + -0.5

Combine like terms: -2.442188714 + -0.5 = -2.942188714
n = -2.942188714

Simplifying
n = -2.942188714


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.942188714, -2.942188714}

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