10n^2+12n-56=-8n

Solution for 10n^2+12n-56=-8n equation:

Simplifying
10n2 + 12n + -56 = -8n

Reorder the terms:
-56 + 12n + 10n2 = -8n

Solving
-56 + 12n + 10n2 = -8n

Solving for variable 'n'.

Reorder the terms:
-56 + 12n + 8n + 10n2 = -8n + 8n

Combine like terms: 12n + 8n = 20n
-56 + 20n + 10n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
-56 + 20n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 10n + 5n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-28 + 10n + 5n2)' equal to zero and attempt to solve:

Simplifying
-28 + 10n + 5n2 = 0

Solving
-28 + 10n + 5n2 = 0

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

Divide each side by '5'.
-5.6 + 2n + n2 = 0

Move the constant term to the right:

Add '5.6' to each side of the equation.
-5.6 + 2n + 5.6 + n2 = 0 + 5.6

Reorder the terms:
-5.6 + 5.6 + 2n + n2 = 0 + 5.6

Combine like terms: -5.6 + 5.6 = 0.0
0.0 + 2n + n2 = 0 + 5.6
2n + n2 = 0 + 5.6

Combine like terms: 0 + 5.6 = 5.6
2n + n2 = 5.6

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 5.6 + 1

Reorder the terms:
1 + 2n + n2 = 5.6 + 1

Combine like terms: 5.6 + 1 = 6.6
1 + 2n + n2 = 6.6

Factor a perfect square on the left side:
(n + 1)(n + 1) = 6.6

Calculate the square root of the right side: 2.569046516

Break this problem into two subproblems by setting 
(n + 1) equal to 2.569046516 and -2.569046516.

Subproblem 1
n + 1 = 2.569046516

Simplifying
n + 1 = 2.569046516

Reorder the terms:
1 + n = 2.569046516

Solving
1 + n = 2.569046516

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 2.569046516 + -1

Combine like terms: 1 + -1 = 0
0 + n = 2.569046516 + -1
n = 2.569046516 + -1

Combine like terms: 2.569046516 + -1 = 1.569046516
n = 1.569046516

Simplifying
n = 1.569046516

Subproblem 2
n + 1 = -2.569046516

Simplifying
n + 1 = -2.569046516

Reorder the terms:
1 + n = -2.569046516

Solving
1 + n = -2.569046516

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -2.569046516 + -1

Combine like terms: 1 + -1 = 0
0 + n = -2.569046516 + -1
n = -2.569046516 + -1

Combine like terms: -2.569046516 + -1 = -3.569046516
n = -3.569046516

Simplifying
n = -3.569046516

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.569046516, -3.569046516}
Solution
n = {1.569046516, -3.569046516}