10n^2+8n-1=3

Solution for 10n^2+8n-1=3 equation:

Simplifying
10n2 + 8n + -1 = 3

Reorder the terms:
-1 + 8n + 10n2 = 3

Solving
-1 + 8n + 10n2 = 3

Solving for variable 'n'.

Reorder the terms:
-1 + -3 + 8n + 10n2 = 3 + -3

Combine like terms: -1 + -3 = -4
-4 + 8n + 10n2 = 3 + -3

Combine like terms: 3 + -3 = 0
-4 + 8n + 10n2 = 0

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

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

Simplifying
-2 + 4n + 5n2 = 0

Solving
-2 + 4n + 5n2 = 0

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

Divide each side by '5'.
-0.4 + 0.8n + n2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.8n + 0.4 + n2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.8n + n2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.8n + n2 = 0 + 0.4
0.8n + n2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.8n + n2 = 0.4

The n term is 0.8n.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8n + 0.16 + n2 = 0.4 + 0.16

Reorder the terms:
0.16 + 0.8n + n2 = 0.4 + 0.16

Combine like terms: 0.4 + 0.16 = 0.56
0.16 + 0.8n + n2 = 0.56

Factor a perfect square on the left side:
(n + 0.4)(n + 0.4) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(n + 0.4) equal to 0.748331477 and -0.748331477.

Subproblem 1
n + 0.4 = 0.748331477

Simplifying
n + 0.4 = 0.748331477

Reorder the terms:
0.4 + n = 0.748331477

Solving
0.4 + n = 0.748331477

Solving for variable 'n'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + n = 0.748331477 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + n = 0.748331477 + -0.4
n = 0.748331477 + -0.4

Combine like terms: 0.748331477 + -0.4 = 0.348331477
n = 0.348331477

Simplifying
n = 0.348331477

Subproblem 2
n + 0.4 = -0.748331477

Simplifying
n + 0.4 = -0.748331477

Reorder the terms:
0.4 + n = -0.748331477

Solving
0.4 + n = -0.748331477

Solving for variable 'n'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + n = -0.748331477 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + n = -0.748331477 + -0.4
n = -0.748331477 + -0.4

Combine like terms: -0.748331477 + -0.4 = -1.148331477
n = -1.148331477

Simplifying
n = -1.148331477

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.348331477, -1.148331477}
Solution
n = {0.348331477, -1.148331477}