-8n^2-6n-12=-9

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Solution for -8n^2-6n-12=-9 equation: 


Simplifying
-8n2 + -6n + -12 = -9

Reorder the terms:
-12 + -6n + -8n2 = -9

Solving
-12 + -6n + -8n2 = -9

Solving for variable 'n'.

Reorder the terms:
-12 + 9 + -6n + -8n2 = -9 + 9

Combine like terms: -12 + 9 = -3
-3 + -6n + -8n2 = -9 + 9

Combine like terms: -9 + 9 = 0
-3 + -6n + -8n2 = 0

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

Ignore the factor -1.

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

Simplifying
3 + 6n + 8n2 = 0

Solving
3 + 6n + 8n2 = 0

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

Divide each side by '8'.
0.375 + 0.75n + n2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 0.75n + -0.375 + n2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 0.75n + n2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 0.75n + n2 = 0 + -0.375
0.75n + n2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
0.75n + n2 = -0.375

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 = -0.375 + 0.140625

Reorder the terms:
0.140625 + 0.75n + n2 = -0.375 + 0.140625

Combine like terms: -0.375 + 0.140625 = -0.234375
0.140625 + 0.75n + n2 = -0.234375

Factor a perfect square on the left side:
(n + 0.375)(n + 0.375) = -0.234375

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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