-8+4n(1+5n)=-6n-14

Solution for -8+4n(1+5n)=-6n-14 equation:

Simplifying
-8 + 4n(1 + 5n) = -6n + -14
-8 + (1 * 4n + 5n * 4n) = -6n + -14
-8 + (4n + 20n2) = -6n + -14

Reorder the terms:
-8 + 4n + 20n2 = -14 + -6n

Solving
-8 + 4n + 20n2 = -14 + -6n

Solving for variable 'n'.

Reorder the terms:
-8 + 14 + 4n + 6n + 20n2 = -14 + -6n + 14 + 6n

Combine like terms: -8 + 14 = 6
6 + 4n + 6n + 20n2 = -14 + -6n + 14 + 6n

Combine like terms: 4n + 6n = 10n
6 + 10n + 20n2 = -14 + -6n + 14 + 6n

Reorder the terms:
6 + 10n + 20n2 = -14 + 14 + -6n + 6n

Combine like terms: -14 + 14 = 0
6 + 10n + 20n2 = 0 + -6n + 6n
6 + 10n + 20n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
6 + 10n + 20n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 5n + 10n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 5n + 10n2)' equal to zero and attempt to solve:

Simplifying
3 + 5n + 10n2 = 0

Solving
3 + 5n + 10n2 = 0

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

Divide each side by '10'.
0.3 + 0.5n + n2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + 0.5n + -0.3 + n2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + 0.5n + n2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + 0.5n + n2 = 0.0 + -0.3
0.5n + n2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
0.5n + n2 = -0.3

The n term is 0.5n.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5n + 0.0625 + n2 = -0.3 + 0.0625

Reorder the terms:
0.0625 + 0.5n + n2 = -0.3 + 0.0625

Combine like terms: -0.3 + 0.0625 = -0.2375
0.0625 + 0.5n + n2 = -0.2375

Factor a perfect square on the left side:
(n + 0.25)(n + 0.25) = -0.2375

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.