6n(n-1)+4=

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Solution for 6n(n-1)+4= equation: 


Simplifying
6n(n + -1) + 4 = 0

Reorder the terms:
6n(-1 + n) + 4 = 0
(-1 * 6n + n * 6n) + 4 = 0
(-6n + 6n2) + 4 = 0

Reorder the terms:
4 + -6n + 6n2 = 0

Solving
4 + -6n + 6n2 = 0

Solving for variable 'n'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -3n + 3n2)' equal to zero and attempt to solve:

Simplifying
2 + -3n + 3n2 = 0

Solving
2 + -3n + 3n2 = 0

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

Divide each side by '3'.
0.6666666667 + -1n + n2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -1n + -0.6666666667 + n2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -1n + n2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -1n + n2 = 0 + -0.6666666667
-1n + n2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-1n + n2 = -0.6666666667

The n term is -1n.  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.
-1n + 0.25 + n2 = -0.6666666667 + 0.25

Reorder the terms:
0.25 + -1n + n2 = -0.6666666667 + 0.25

Combine like terms: -0.6666666667 + 0.25 = -0.4166666667
0.25 + -1n + n2 = -0.4166666667

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = -0.4166666667

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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