8n(-2n-3)=12

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Solution for 8n(-2n-3)=12 equation: 


Simplifying
8n(-2n + -3) = 12

Reorder the terms:
8n(-3 + -2n) = 12
(-3 * 8n + -2n * 8n) = 12
(-24n + -16n2) = 12

Solving
-24n + -16n2 = 12

Solving for variable 'n'.

Reorder the terms:
-12 + -24n + -16n2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -24n + -16n2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(3 + 6n + 4n2) = 0

Ignore the factor -4.

Subproblem 1
Set the factor '(3 + 6n + 4n2)' equal to zero and attempt to solve:

Simplifying
3 + 6n + 4n2 = 0

Solving
3 + 6n + 4n2 = 0

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

Divide each side by '4'.
0.75 + 1.5n + n2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 1.5n + -0.75 + n2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 1.5n + n2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 1.5n + n2 = 0 + -0.75
1.5n + n2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
1.5n + n2 = -0.75

The n term is 1.5n.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5n + 0.5625 + n2 = -0.75 + 0.5625

Reorder the terms:
0.5625 + 1.5n + n2 = -0.75 + 0.5625

Combine like terms: -0.75 + 0.5625 = -0.1875
0.5625 + 1.5n + n2 = -0.1875

Factor a perfect square on the left side:
(n + 0.75)(n + 0.75) = -0.1875

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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