10n^2+20n=-26

Solution for 10n^2+20n=-26 equation:

Simplifying
10n2 + 20n = -26

Reorder the terms:
20n + 10n2 = -26

Solving
20n + 10n2 = -26

Solving for variable 'n'.

Reorder the terms:
26 + 20n + 10n2 = -26 + 26

Combine like terms: -26 + 26 = 0
26 + 20n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + 10n + 5n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(13 + 10n + 5n2)' equal to zero and attempt to solve:

Simplifying
13 + 10n + 5n2 = 0

Solving
13 + 10n + 5n2 = 0

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

Divide each side by '5'.
2.6 + 2n + n2 = 0

Move the constant term to the right:

Add '-2.6' to each side of the equation.
2.6 + 2n + -2.6 + n2 = 0 + -2.6

Reorder the terms:
2.6 + -2.6 + 2n + n2 = 0 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + 2n + n2 = 0 + -2.6
2n + n2 = 0 + -2.6

Combine like terms: 0 + -2.6 = -2.6
2n + n2 = -2.6

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 = -2.6 + 1

Reorder the terms:
1 + 2n + n2 = -2.6 + 1

Combine like terms: -2.6 + 1 = -1.6
1 + 2n + n2 = -1.6

Factor a perfect square on the left side:
(n + 1)(n + 1) = -1.6

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.