8n(-5n+7)=8

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


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

Reorder the terms:
8n(7 + -5n) = 8
(7 * 8n + -5n * 8n) = 8
(56n + -40n2) = 8

Solving
56n + -40n2 = 8

Solving for variable 'n'.

Reorder the terms:
-8 + 56n + -40n2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 56n + -40n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + 7n + -5n2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-1 + 7n + -5n2)' equal to zero and attempt to solve:

Simplifying
-1 + 7n + -5n2 = 0

Solving
-1 + 7n + -5n2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.2 + -1.4n + n2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1.4n + -0.2 + n2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1.4n + n2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1.4n + n2 = 0 + -0.2
-1.4n + n2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1.4n + n2 = -0.2

The n term is -1.4n.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4n + 0.49 + n2 = -0.2 + 0.49

Reorder the terms:
0.49 + -1.4n + n2 = -0.2 + 0.49

Combine like terms: -0.2 + 0.49 = 0.29
0.49 + -1.4n + n2 = 0.29

Factor a perfect square on the left side:
(n + -0.7)(n + -0.7) = 0.29

Calculate the square root of the right side: 0.538516481

Break this problem into two subproblems by setting 
(n + -0.7) equal to 0.538516481 and -0.538516481.


Subproblem 1
n + -0.7 = 0.538516481

Simplifying
n + -0.7 = 0.538516481

Reorder the terms:
-0.7 + n = 0.538516481

Solving
-0.7 + n = 0.538516481

Solving for variable 'n'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + n = 0.538516481 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + n = 0.538516481 + 0.7
n = 0.538516481 + 0.7

Combine like terms: 0.538516481 + 0.7 = 1.238516481
n = 1.238516481

Simplifying
n = 1.238516481


Subproblem 2
n + -0.7 = -0.538516481

Simplifying
n + -0.7 = -0.538516481

Reorder the terms:
-0.7 + n = -0.538516481

Solving
-0.7 + n = -0.538516481

Solving for variable 'n'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + n = -0.538516481 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + n = -0.538516481 + 0.7
n = -0.538516481 + 0.7

Combine like terms: -0.538516481 + 0.7 = 0.161483519
n = 0.161483519

Simplifying
n = 0.161483519


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.238516481, 0.161483519}
Solution
n = {1.238516481, 0.161483519}

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