-4n(3n+1)=4

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Solution for -4n(3n+1)=4 equation: 


Simplifying
-4n(3n + 1) = 4

Reorder the terms:
-4n(1 + 3n) = 4
(1 * -4n + 3n * -4n) = 4
(-4n + -12n2) = 4

Solving
-4n + -12n2 = 4

Solving for variable 'n'.

Reorder the terms:
-4 + -4n + -12n2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -4n + -12n2 = 0

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

Ignore the factor -4.

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

Simplifying
1 + n + 3n2 = 0

Solving
1 + n + 3n2 = 0

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

Divide each side by '3'.
0.3333333333 + 0.3333333333n + n2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 0.3333333333n + -0.3333333333 + n2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 0.3333333333n + n2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 0.3333333333n + n2 = 0 + -0.3333333333
0.3333333333n + n2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
0.3333333333n + n2 = -0.3333333333

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

Add '0.25' to each side of the equation.
0.3333333333n + 0.25 + n2 = -0.3333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333n + n2 = -0.3333333333 + 0.25

Combine like terms: -0.3333333333 + 0.25 = -0.0833333333
0.25 + 0.3333333333n + n2 = -0.0833333333

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -0.0833333333

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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