x-(4-3x)=6x(x-2)

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


Simplifying
x + -1(4 + -3x) = 6x(x + -2)
x + (4 * -1 + -3x * -1) = 6x(x + -2)
x + (-4 + 3x) = 6x(x + -2)

Reorder the terms:
-4 + x + 3x = 6x(x + -2)

Combine like terms: x + 3x = 4x
-4 + 4x = 6x(x + -2)

Reorder the terms:
-4 + 4x = 6x(-2 + x)
-4 + 4x = (-2 * 6x + x * 6x)
-4 + 4x = (-12x + 6x2)

Solving
-4 + 4x = -12x + 6x2

Solving for variable 'x'.

Combine like terms: 4x + 12x = 16x
-4 + 16x + -6x2 = -12x + 6x2 + 12x + -6x2

Reorder the terms:
-4 + 16x + -6x2 = -12x + 12x + 6x2 + -6x2

Combine like terms: -12x + 12x = 0
-4 + 16x + -6x2 = 0 + 6x2 + -6x2
-4 + 16x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-4 + 16x + -6x2 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 8x + -3x2)' equal to zero and attempt to solve:

Simplifying
-2 + 8x + -3x2 = 0

Solving
-2 + 8x + -3x2 = 0

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

Divide each side by '-3'.
0.6666666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -2.666666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -2.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -2.666666667x + x2 = 0 + -0.6666666667
-2.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-2.666666667x + x2 = -0.6666666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -0.6666666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -0.6666666667 + 1.777777780

Combine like terms: -0.6666666667 + 1.777777780 = 1.1111111133
1.777777780 + -2.666666667x + x2 = 1.1111111133

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 1.1111111133

Calculate the square root of the right side: 1.054092554

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 1.054092554 and -1.054092554.


Subproblem 1
x + -1.333333334 = 1.054092554

Simplifying
x + -1.333333334 = 1.054092554

Reorder the terms:
-1.333333334 + x = 1.054092554

Solving
-1.333333334 + x = 1.054092554

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 1.054092554 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 1.054092554 + 1.333333334
x = 1.054092554 + 1.333333334

Combine like terms: 1.054092554 + 1.333333334 = 2.387425888
x = 2.387425888

Simplifying
x = 2.387425888


Subproblem 2
x + -1.333333334 = -1.054092554

Simplifying
x + -1.333333334 = -1.054092554

Reorder the terms:
-1.333333334 + x = -1.054092554

Solving
-1.333333334 + x = -1.054092554

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -1.054092554 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -1.054092554 + 1.333333334
x = -1.054092554 + 1.333333334

Combine like terms: -1.054092554 + 1.333333334 = 0.27924078
x = 0.27924078

Simplifying
x = 0.27924078


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.387425888, 0.27924078}
Solution
x = {2.387425888, 0.27924078}

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