12n^2-3n+6=0

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Solution for 12n^2-3n+6=0 equation: 


Simplifying
12n2 + -3n + 6 = 0

Reorder the terms:
6 + -3n + 12n2 = 0

Solving
6 + -3n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -1n + 4n2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -1n + 4n2)' equal to zero and attempt to solve:

Simplifying
2 + -1n + 4n2 = 0

Solving
2 + -1n + 4n2 = 0

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

Divide each side by '4'.
0.5 + -0.25n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -0.25n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -0.25n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -0.25n + n2 = 0 + -0.5
-0.25n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-0.25n + n2 = -0.5

The n term is -0.25n.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25n + 0.015625 + n2 = -0.5 + 0.015625

Reorder the terms:
0.015625 + -0.25n + n2 = -0.5 + 0.015625

Combine like terms: -0.5 + 0.015625 = -0.484375
0.015625 + -0.25n + n2 = -0.484375

Factor a perfect square on the left side:
(n + -0.125)(n + -0.125) = -0.484375

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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