n(8n+4)=-4

Solution for n(8n+4)=-4 equation:

Simplifying
n(8n + 4) = -4

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

Solving
4n + 8n2 = -4

Solving for variable 'n'.

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + n + 2n2) = 0

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

Simplifying
1 + n + 2n2 = 0

Solving
1 + n + 2n2 = 0

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

Divide each side by '2'.
0.5 + 0.5n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.5n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.5n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.5n + n2 = 0 + -0.5
0.5n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.5n + n2 = -0.5

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5n + 0.25 + n2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.5n + n2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.5n + n2 = -0.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -0.25

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.