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

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

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

Reorder the terms:
3x + -1(6 + -2x) = 4x(x + -4) + x
3x + (6 * -1 + -2x * -1) = 4x(x + -4) + x
3x + (-6 + 2x) = 4x(x + -4) + x

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

Combine like terms: 3x + 2x = 5x
-6 + 5x = 4x(x + -4) + x

Reorder the terms:
-6 + 5x = 4x(-4 + x) + x
-6 + 5x = (-4 * 4x + x * 4x) + x
-6 + 5x = (-16x + 4x2) + x

Reorder the terms:
-6 + 5x = -16x + x + 4x2

Combine like terms: -16x + x = -15x
-6 + 5x = -15x + 4x2

Solving
-6 + 5x = -15x + 4x2

Solving for variable 'x'.

Combine like terms: 5x + 15x = 20x
-6 + 20x + -4x2 = -15x + 4x2 + 15x + -4x2

Reorder the terms:
-6 + 20x + -4x2 = -15x + 15x + 4x2 + -4x2

Combine like terms: -15x + 15x = 0
-6 + 20x + -4x2 = 0 + 4x2 + -4x2
-6 + 20x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6 + 20x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 10x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 10x + -2x2)' equal to zero and attempt to solve:

Simplifying
-3 + 10x + -2x2 = 0

Solving
-3 + 10x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1.5 + -5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -5x + x2 = 0 + -1.5
-5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-5x + x2 = -1.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -1.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -1.5 + 6.25

Combine like terms: -1.5 + 6.25 = 4.75
6.25 + -5x + x2 = 4.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.179449472 and -2.179449472.

Subproblem 1
x + -2.5 = 2.179449472

Simplifying
x + -2.5 = 2.179449472

Reorder the terms:
-2.5 + x = 2.179449472

Solving
-2.5 + x = 2.179449472

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.179449472 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.179449472 + 2.5
x = 2.179449472 + 2.5

Combine like terms: 2.179449472 + 2.5 = 4.679449472
x = 4.679449472

Simplifying
x = 4.679449472

Subproblem 2
x + -2.5 = -2.179449472

Simplifying
x + -2.5 = -2.179449472

Reorder the terms:
-2.5 + x = -2.179449472

Solving
-2.5 + x = -2.179449472

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.179449472 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.179449472 + 2.5
x = -2.179449472 + 2.5

Combine like terms: -2.179449472 + 2.5 = 0.320550528
x = 0.320550528

Simplifying
x = 0.320550528

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.679449472, 0.320550528}
Solution
x = {4.679449472, 0.320550528}