4x*4x+12x+6=0

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Solution for 4x*4x+12x+6=0 equation: 


Simplifying
4x * 4x + 12x + 6 = 0

Reorder the terms for easier multiplication:
4 * 4x * x + 12x + 6 = 0

Multiply 4 * 4
16x * x + 12x + 6 = 0

Multiply x * x
16x2 + 12x + 6 = 0

Reorder the terms:
6 + 12x + 16x2 = 0

Solving
6 + 12x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 6x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + 6x + 8x2)' equal to zero and attempt to solve:

Simplifying
3 + 6x + 8x2 = 0

Solving
3 + 6x + 8x2 = 0

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

Divide each side by '8'.
0.375 + 0.75x + x2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 0.75x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 0.75x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 0.75x + x2 = 0 + -0.375
0.75x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
0.75x + x2 = -0.375

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = -0.375 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = -0.375 + 0.140625

Combine like terms: -0.375 + 0.140625 = -0.234375
0.140625 + 0.75x + x2 = -0.234375

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = -0.234375

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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