0=4-4x-6x^2

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Solution for 0=4-4x-6x^2 equation: 


Simplifying
0 = 4 + -4x + -6x2

Solving
0 = 4 + -4x + -6x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + 4x + 6x2 = 4 + -4x + -6x2 + -4 + 4x + 6x2

Reorder the terms:
-4 + 4x + 6x2 = 4 + -4 + -4x + 4x + -6x2 + 6x2

Combine like terms: 4 + -4 = 0
-4 + 4x + 6x2 = 0 + -4x + 4x + -6x2 + 6x2
-4 + 4x + 6x2 = -4x + 4x + -6x2 + 6x2

Combine like terms: -4x + 4x = 0
-4 + 4x + 6x2 = 0 + -6x2 + 6x2
-4 + 4x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-4 + 4x + 6x2 = 0

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

Ignore the factor 2.

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

Simplifying
-2 + 2x + 3x2 = 0

Solving
-2 + 2x + 3x2 = 0

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

Divide each side by '3'.
-0.6666666667 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 0.6666666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 0.6666666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 0.6666666667x + x2 = 0 + 0.6666666667
0.6666666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
0.6666666667x + x2 = 0.6666666667

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 0.6666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.6666666667 + 0.1111111112

Combine like terms: 0.6666666667 + 0.1111111112 = 0.7777777779
0.1111111112 + 0.6666666667x + x2 = 0.7777777779

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.7777777779

Calculate the square root of the right side: 0.881917104

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.881917104 and -0.881917104.


Subproblem 1
x + 0.3333333334 = 0.881917104

Simplifying
x + 0.3333333334 = 0.881917104

Reorder the terms:
0.3333333334 + x = 0.881917104

Solving
0.3333333334 + x = 0.881917104

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.881917104 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.881917104 + -0.3333333334
x = 0.881917104 + -0.3333333334

Combine like terms: 0.881917104 + -0.3333333334 = 0.5485837706
x = 0.5485837706

Simplifying
x = 0.5485837706


Subproblem 2
x + 0.3333333334 = -0.881917104

Simplifying
x + 0.3333333334 = -0.881917104

Reorder the terms:
0.3333333334 + x = -0.881917104

Solving
0.3333333334 + x = -0.881917104

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.881917104 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.881917104 + -0.3333333334
x = -0.881917104 + -0.3333333334

Combine like terms: -0.881917104 + -0.3333333334 = -1.2152504374
x = -1.2152504374

Simplifying
x = -1.2152504374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5485837706, -1.2152504374}
Solution
x = {0.5485837706, -1.2152504374}

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