-5n(5n+8)=5

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


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

Reorder the terms:
-5n(8 + 5n) = 5
(8 * -5n + 5n * -5n) = 5
(-40n + -25n2) = 5

Solving
-40n + -25n2 = 5

Solving for variable 'n'.

Reorder the terms:
-5 + -40n + -25n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -40n + -25n2 = 0

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

Ignore the factor -5.

Subproblem 1
Set the factor '(1 + 8n + 5n2)' equal to zero and attempt to solve:

Simplifying
1 + 8n + 5n2 = 0

Solving
1 + 8n + 5n2 = 0

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

Divide each side by '5'.
0.2 + 1.6n + n2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.6n + -0.2 + n2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.6n + n2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.6n + n2 = 0 + -0.2
1.6n + n2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
1.6n + n2 = -0.2

The n term is 1.6n.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6n + 0.64 + n2 = -0.2 + 0.64

Reorder the terms:
0.64 + 1.6n + n2 = -0.2 + 0.64

Combine like terms: -0.2 + 0.64 = 0.44
0.64 + 1.6n + n2 = 0.44

Factor a perfect square on the left side:
(n + 0.8)(n + 0.8) = 0.44

Calculate the square root of the right side: 0.663324958

Break this problem into two subproblems by setting 
(n + 0.8) equal to 0.663324958 and -0.663324958.


Subproblem 1
n + 0.8 = 0.663324958

Simplifying
n + 0.8 = 0.663324958

Reorder the terms:
0.8 + n = 0.663324958

Solving
0.8 + n = 0.663324958

Solving for variable 'n'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + n = 0.663324958 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + n = 0.663324958 + -0.8
n = 0.663324958 + -0.8

Combine like terms: 0.663324958 + -0.8 = -0.136675042
n = -0.136675042

Simplifying
n = -0.136675042


Subproblem 2
n + 0.8 = -0.663324958

Simplifying
n + 0.8 = -0.663324958

Reorder the terms:
0.8 + n = -0.663324958

Solving
0.8 + n = -0.663324958

Solving for variable 'n'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + n = -0.663324958 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + n = -0.663324958 + -0.8
n = -0.663324958 + -0.8

Combine like terms: -0.663324958 + -0.8 = -1.463324958
n = -1.463324958

Simplifying
n = -1.463324958


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.136675042, -1.463324958}
Solution
n = {-0.136675042, -1.463324958}

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