-2n(4n+1)=4

Solution for -2n(4n+1)=4 equation:

Simplifying
-2n(4n + 1) = 4

Reorder the terms:
-2n(1 + 4n) = 4
(1 * -2n + 4n * -2n) = 4
(-2n + -8n2) = 4

Solving
-2n + -8n2 = 4

Solving for variable 'n'.

Reorder the terms:
-4 + -2n + -8n2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -2n + -8n2 = 0

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

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

Simplifying
2 + n + 4n2 = 0

Solving
2 + n + 4n2 = 0

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

Divide each side by '4'.
0.5 + 0.25n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.25n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.25n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.25n + n2 = 0 + -0.5
0.25n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.25n + 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.
0.25n + 0.25 + n2 = -0.5 + 0.25

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

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