-3n^2-8n-14=-8

Solution for -3n^2-8n-14=-8 equation:

Simplifying
-3n2 + -8n + -14 = -8

Reorder the terms:
-14 + -8n + -3n2 = -8

Solving
-14 + -8n + -3n2 = -8

Solving for variable 'n'.

Reorder the terms:
-14 + 8 + -8n + -3n2 = -8 + 8

Combine like terms: -14 + 8 = -6
-6 + -8n + -3n2 = -8 + 8

Combine like terms: -8 + 8 = 0
-6 + -8n + -3n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 8n + 3n2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 8n + 3n2)' equal to zero and attempt to solve:

Simplifying
6 + 8n + 3n2 = 0

Solving
6 + 8n + 3n2 = 0

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

Divide each side by '3'.
2 + 2.666666667n + n2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2.666666667n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + 2.666666667n + n2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2.666666667n + n2 = 0 + -2
2.666666667n + n2 = 0 + -2

Combine like terms: 0 + -2 = -2
2.666666667n + n2 = -2

The n term is 2.666666667n.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667n + 1.777777780 + n2 = -2 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667n + n2 = -2 + 1.777777780

Combine like terms: -2 + 1.777777780 = -0.22222222
1.777777780 + 2.666666667n + n2 = -0.22222222

Factor a perfect square on the left side:
(n + 1.333333334)(n + 1.333333334) = -0.22222222

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.