10n^2-6=-10n

Solution for 10n^2-6=-10n equation:

Simplifying
10n2 + -6 = -10n

Reorder the terms:
-6 + 10n2 = -10n

Solving
-6 + 10n2 = -10n

Solving for variable 'n'.

Reorder the terms:
-6 + 10n + 10n2 = -10n + 10n

Combine like terms: -10n + 10n = 0
-6 + 10n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 5n + 5n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 5n + 5n2)' equal to zero and attempt to solve:

Simplifying
-3 + 5n + 5n2 = 0

Solving
-3 + 5n + 5n2 = 0

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

Divide each side by '5'.
-0.6 + n + n2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + n + 0.6 + n2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + n + n2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + n + n2 = 0 + 0.6
n + n2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
n + n2 = 0.6

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 = 0.6 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + n2 = 0.6 + 0.25

Combine like terms: 0.6 + 0.25 = 0.85
1.25 + n2 = 0.85

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 0.85

Calculate the square root of the right side: 0.921954446

Break this problem into two subproblems by setting 
(n + 0.5) equal to 0.921954446 and -0.921954446.

Subproblem 1
n + 0.5 = 0.921954446

Simplifying
n + 0.5 = 0.921954446

Reorder the terms:
0.5 + n = 0.921954446

Solving
0.5 + n = 0.921954446

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 = 0.921954446 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 0.921954446 + -0.5
n = 0.921954446 + -0.5

Combine like terms: 0.921954446 + -0.5 = 0.421954446
n = 0.421954446

Simplifying
n = 0.421954446

Subproblem 2
n + 0.5 = -0.921954446

Simplifying
n + 0.5 = -0.921954446

Reorder the terms:
0.5 + n = -0.921954446

Solving
0.5 + n = -0.921954446

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 = -0.921954446 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -0.921954446 + -0.5
n = -0.921954446 + -0.5

Combine like terms: -0.921954446 + -0.5 = -1.421954446
n = -1.421954446

Simplifying
n = -1.421954446

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.421954446, -1.421954446}
Solution
n = {0.421954446, -1.421954446}