3x-4(x+1)=-(6x+4)x

Solution for 3x-4(x+1)=-(6x+4)x equation:

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

Reorder the terms:
3x + -4(1 + x) = -1(6x + 4) * x
3x + (1 * -4 + x * -4) = -1(6x + 4) * x
3x + (-4 + -4x) = -1(6x + 4) * x

Reorder the terms:
-4 + 3x + -4x = -1(6x + 4) * x

Combine like terms: 3x + -4x = -1x
-4 + -1x = -1(6x + 4) * x

Reorder the terms:
-4 + -1x = -1(4 + 6x) * x

Reorder the terms for easier multiplication:
-4 + -1x = -1x(4 + 6x)
-4 + -1x = (4 * -1x + 6x * -1x)
-4 + -1x = (-4x + -6x2)

Solving
-4 + -1x = -4x + -6x2

Solving for variable 'x'.

Combine like terms: -1x + 4x = 3x
-4 + 3x + 6x2 = -4x + -6x2 + 4x + 6x2

Reorder the terms:
-4 + 3x + 6x2 = -4x + 4x + -6x2 + 6x2

Combine like terms: -4x + 4x = 0
-4 + 3x + 6x2 = 0 + -6x2 + 6x2
-4 + 3x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-4 + 3x + 6x2 = 0

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

Divide each side by '6'.
-0.6666666667 + 0.5x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 0.5x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 0.5x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 0.5x + x2 = 0 + 0.6666666667
0.5x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
0.5x + x2 = 0.6666666667

The x term is 0.5x.  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.
0.5x + 0.0625 + x2 = 0.6666666667 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.6666666667 + 0.0625

Combine like terms: 0.6666666667 + 0.0625 = 0.7291666667
0.0625 + 0.5x + x2 = 0.7291666667

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.7291666667

Calculate the square root of the right side: 0.853912564

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.853912564 and -0.853912564.

Subproblem 1
x + 0.25 = 0.853912564

Simplifying
x + 0.25 = 0.853912564

Reorder the terms:
0.25 + x = 0.853912564

Solving
0.25 + x = 0.853912564

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.853912564 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.853912564 + -0.25
x = 0.853912564 + -0.25

Combine like terms: 0.853912564 + -0.25 = 0.603912564
x = 0.603912564

Simplifying
x = 0.603912564

Subproblem 2
x + 0.25 = -0.853912564

Simplifying
x + 0.25 = -0.853912564

Reorder the terms:
0.25 + x = -0.853912564

Solving
0.25 + x = -0.853912564

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.853912564 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.853912564 + -0.25
x = -0.853912564 + -0.25

Combine like terms: -0.853912564 + -0.25 = -1.103912564
x = -1.103912564

Simplifying
x = -1.103912564

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.603912564, -1.103912564}