-2n(2n+4)=10

Solution for -2n(2n+4)=10 equation:

Simplifying
-2n(2n + 4) = 10

Reorder the terms:
-2n(4 + 2n) = 10
(4 * -2n + 2n * -2n) = 10
(-8n + -4n2) = 10

Solving
-8n + -4n2 = 10

Solving for variable 'n'.

Reorder the terms:
-10 + -8n + -4n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -8n + -4n2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(5 + 4n + 2n2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(5 + 4n + 2n2)' equal to zero and attempt to solve:

Simplifying
5 + 4n + 2n2 = 0

Solving
5 + 4n + 2n2 = 0

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

Divide each side by '2'.
2.5 + 2n + n2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 2n + -2.5 + n2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 2n + n2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 2n + n2 = 0 + -2.5
2n + n2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
2n + n2 = -2.5

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 = -2.5 + 1

Reorder the terms:
1 + 2n + n2 = -2.5 + 1

Combine like terms: -2.5 + 1 = -1.5
1 + 2n + n2 = -1.5

Factor a perfect square on the left side:
(n + 1)(n + 1) = -1.5

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.