8n^2+8n-10=0

Solution for 8n^2+8n-10=0 equation:

Simplifying
8n2 + 8n + -10 = 0

Reorder the terms:
-10 + 8n + 8n2 = 0

Solving
-10 + 8n + 8n2 = 0

Solving for variable 'n'.

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 4n + 4n2)' equal to zero and attempt to solve:

Simplifying
-5 + 4n + 4n2 = 0

Solving
-5 + 4n + 4n2 = 0

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

Divide each side by '4'.
-1.25 + n + n2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + n + 1.25 + n2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + n + n2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + n + n2 = 0 + 1.25
n + n2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
n + n2 = 1.25

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 = 1.25 + 0.25

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

Combine like terms: 1.25 + 0.25 = 1.5
1.25 + n2 = 1.5

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(n + 0.5) equal to 1.224744871 and -1.224744871.

Subproblem 1
n + 0.5 = 1.224744871

Simplifying
n + 0.5 = 1.224744871

Reorder the terms:
0.5 + n = 1.224744871

Solving
0.5 + n = 1.224744871

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 = 1.224744871 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 1.224744871 + -0.5
n = 1.224744871 + -0.5

Combine like terms: 1.224744871 + -0.5 = 0.724744871
n = 0.724744871

Simplifying
n = 0.724744871

Subproblem 2
n + 0.5 = -1.224744871

Simplifying
n + 0.5 = -1.224744871

Reorder the terms:
0.5 + n = -1.224744871

Solving
0.5 + n = -1.224744871

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 = -1.224744871 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -1.224744871 + -0.5
n = -1.224744871 + -0.5

Combine like terms: -1.224744871 + -0.5 = -1.724744871
n = -1.724744871

Simplifying
n = -1.724744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.724744871, -1.724744871}
Solution
n = {0.724744871, -1.724744871}