10n^2+12n-12=0

Solution for 10n^2+12n-12=0 equation:

Simplifying
10n2 + 12n + -12 = 0

Reorder the terms:
-12 + 12n + 10n2 = 0

Solving
-12 + 12n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 6n + 5n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 6n + 5n2)' equal to zero and attempt to solve:

Simplifying
-6 + 6n + 5n2 = 0

Solving
-6 + 6n + 5n2 = 0

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

Divide each side by '5'.
-1.2 + 1.2n + n2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 1.2n + 1.2 + n2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 1.2n + n2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 1.2n + n2 = 0 + 1.2
1.2n + n2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
1.2n + n2 = 1.2

The n term is 1.2n.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2n + 0.36 + n2 = 1.2 + 0.36

Reorder the terms:
0.36 + 1.2n + n2 = 1.2 + 0.36

Combine like terms: 1.2 + 0.36 = 1.56
0.36 + 1.2n + n2 = 1.56

Factor a perfect square on the left side:
(n + 0.6)(n + 0.6) = 1.56

Calculate the square root of the right side: 1.2489996

Break this problem into two subproblems by setting 
(n + 0.6) equal to 1.2489996 and -1.2489996.

Subproblem 1
n + 0.6 = 1.2489996

Simplifying
n + 0.6 = 1.2489996

Reorder the terms:
0.6 + n = 1.2489996

Solving
0.6 + n = 1.2489996

Solving for variable 'n'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + n = 1.2489996 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + n = 1.2489996 + -0.6
n = 1.2489996 + -0.6

Combine like terms: 1.2489996 + -0.6 = 0.6489996
n = 0.6489996

Simplifying
n = 0.6489996

Subproblem 2
n + 0.6 = -1.2489996

Simplifying
n + 0.6 = -1.2489996

Reorder the terms:
0.6 + n = -1.2489996

Solving
0.6 + n = -1.2489996

Solving for variable 'n'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + n = -1.2489996 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + n = -1.2489996 + -0.6
n = -1.2489996 + -0.6

Combine like terms: -1.2489996 + -0.6 = -1.8489996
n = -1.8489996

Simplifying
n = -1.8489996

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.6489996, -1.8489996}
Solution
n = {0.6489996, -1.8489996}