2n^2=-10n-6

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

Simplifying
2n2 = -10n + -6

Reorder the terms:
2n2 = -6 + -10n

Solving
2n2 = -6 + -10n

Solving for variable 'n'.

Reorder the terms:
6 + 10n + 2n2 = -6 + -10n + 6 + 10n

Reorder the terms:
6 + 10n + 2n2 = -6 + 6 + -10n + 10n

Combine like terms: -6 + 6 = 0
6 + 10n + 2n2 = 0 + -10n + 10n
6 + 10n + 2n2 = -10n + 10n

Combine like terms: -10n + 10n = 0
6 + 10n + 2n2 = 0

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

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

Simplifying
3 + 5n + n2 = 0

Solving
3 + 5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 5n + -3 + n2 = 0 + -3

Reorder the terms:
3 + -3 + 5n + n2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5n + n2 = 0 + -3
5n + n2 = 0 + -3

Combine like terms: 0 + -3 = -3
5n + n2 = -3

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = -3 + 6.25

Reorder the terms:
6.25 + 5n + n2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + 5n + n2 = 3.25

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(n + 2.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
n + 2.5 = 1.802775638

Simplifying
n + 2.5 = 1.802775638

Reorder the terms:
2.5 + n = 1.802775638

Solving
2.5 + n = 1.802775638

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = 1.802775638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = 1.802775638 + -2.5
n = 1.802775638 + -2.5

Combine like terms: 1.802775638 + -2.5 = -0.697224362
n = -0.697224362

Simplifying
n = -0.697224362

Subproblem 2
n + 2.5 = -1.802775638

Simplifying
n + 2.5 = -1.802775638

Reorder the terms:
2.5 + n = -1.802775638

Solving
2.5 + n = -1.802775638

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = -1.802775638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = -1.802775638 + -2.5
n = -1.802775638 + -2.5

Combine like terms: -1.802775638 + -2.5 = -4.302775638
n = -4.302775638

Simplifying
n = -4.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.697224362, -4.302775638}
Solution
n = {-0.697224362, -4.302775638}