12p^2+6p+2=0

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Solution for 12p^2+6p+2=0 equation: 


Simplifying
12p2 + 6p + 2 = 0

Reorder the terms:
2 + 6p + 12p2 = 0

Solving
2 + 6p + 12p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 3p + 6p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 3p + 6p2)' equal to zero and attempt to solve:

Simplifying
1 + 3p + 6p2 = 0

Solving
1 + 3p + 6p2 = 0

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

Divide each side by '6'.
0.1666666667 + 0.5p + p2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 0.5p + -0.1666666667 + p2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 0.5p + p2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 0.5p + p2 = 0 + -0.1666666667
0.5p + p2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
0.5p + p2 = -0.1666666667

The p term is 0.5p.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5p + 0.0625 + p2 = -0.1666666667 + 0.0625

Reorder the terms:
0.0625 + 0.5p + p2 = -0.1666666667 + 0.0625

Combine like terms: -0.1666666667 + 0.0625 = -0.1041666667
0.0625 + 0.5p + p2 = -0.1041666667

Factor a perfect square on the left side:
(p + 0.25)(p + 0.25) = -0.1041666667

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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