2x(3x+4)+6=

Solution for 2x(3x+4)+6= equation:

Simplifying
2x(3x + 4) + 6 = 0

Reorder the terms:
2x(4 + 3x) + 6 = 0
(4 * 2x + 3x * 2x) + 6 = 0
(8x + 6x2) + 6 = 0

Reorder the terms:
6 + 8x + 6x2 = 0

Solving
6 + 8x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 4x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 4x + 3x2)' equal to zero and attempt to solve:

Simplifying
3 + 4x + 3x2 = 0

Solving
3 + 4x + 3x2 = 0

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

Divide each side by '3'.
1 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.333333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 1.333333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.333333333x + x2 = 0 + -1
1.333333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
1.333333333x + x2 = -1

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = -1 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = -1 + 0.4444444442

Combine like terms: -1 + 0.4444444442 = -0.5555555558
0.4444444442 + 1.333333333x + x2 = -0.5555555558

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = -0.5555555558

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.