8n^2+6n+2=0

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Solution for 8n^2+6n+2=0 equation: 


Simplifying
8n2 + 6n + 2 = 0

Reorder the terms:
2 + 6n + 8n2 = 0

Solving
2 + 6n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 3n + 4n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 3n + 4n2)' equal to zero and attempt to solve:

Simplifying
1 + 3n + 4n2 = 0

Solving
1 + 3n + 4n2 = 0

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

Divide each side by '4'.
0.25 + 0.75n + n2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 0.75n + -0.25 + n2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 0.75n + n2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 0.75n + n2 = 0 + -0.25
0.75n + n2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
0.75n + n2 = -0.25

The n term is 0.75n.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75n + 0.140625 + n2 = -0.25 + 0.140625

Reorder the terms:
0.140625 + 0.75n + n2 = -0.25 + 0.140625

Combine like terms: -0.25 + 0.140625 = -0.109375
0.140625 + 0.75n + n2 = -0.109375

Factor a perfect square on the left side:
(n + 0.375)(n + 0.375) = -0.109375

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.

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