3x(x-2)+4(2x-6)=6(x-4)+8(2x+1)

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Solution for 3x(x-2)+4(2x-6)=6(x-4)+8(2x+1) equation: 


Simplifying
3x(x + -2) + 4(2x + -6) = 6(x + -4) + 8(2x + 1)

Reorder the terms:
3x(-2 + x) + 4(2x + -6) = 6(x + -4) + 8(2x + 1)
(-2 * 3x + x * 3x) + 4(2x + -6) = 6(x + -4) + 8(2x + 1)
(-6x + 3x2) + 4(2x + -6) = 6(x + -4) + 8(2x + 1)

Reorder the terms:
-6x + 3x2 + 4(-6 + 2x) = 6(x + -4) + 8(2x + 1)
-6x + 3x2 + (-6 * 4 + 2x * 4) = 6(x + -4) + 8(2x + 1)
-6x + 3x2 + (-24 + 8x) = 6(x + -4) + 8(2x + 1)

Reorder the terms:
-24 + -6x + 8x + 3x2 = 6(x + -4) + 8(2x + 1)

Combine like terms: -6x + 8x = 2x
-24 + 2x + 3x2 = 6(x + -4) + 8(2x + 1)

Reorder the terms:
-24 + 2x + 3x2 = 6(-4 + x) + 8(2x + 1)
-24 + 2x + 3x2 = (-4 * 6 + x * 6) + 8(2x + 1)
-24 + 2x + 3x2 = (-24 + 6x) + 8(2x + 1)

Reorder the terms:
-24 + 2x + 3x2 = -24 + 6x + 8(1 + 2x)
-24 + 2x + 3x2 = -24 + 6x + (1 * 8 + 2x * 8)
-24 + 2x + 3x2 = -24 + 6x + (8 + 16x)

Reorder the terms:
-24 + 2x + 3x2 = -24 + 8 + 6x + 16x

Combine like terms: -24 + 8 = -16
-24 + 2x + 3x2 = -16 + 6x + 16x

Combine like terms: 6x + 16x = 22x
-24 + 2x + 3x2 = -16 + 22x

Solving
-24 + 2x + 3x2 = -16 + 22x

Solving for variable 'x'.

Reorder the terms:
-24 + 16 + 2x + -22x + 3x2 = -16 + 22x + 16 + -22x

Combine like terms: -24 + 16 = -8
-8 + 2x + -22x + 3x2 = -16 + 22x + 16 + -22x

Combine like terms: 2x + -22x = -20x
-8 + -20x + 3x2 = -16 + 22x + 16 + -22x

Reorder the terms:
-8 + -20x + 3x2 = -16 + 16 + 22x + -22x

Combine like terms: -16 + 16 = 0
-8 + -20x + 3x2 = 0 + 22x + -22x
-8 + -20x + 3x2 = 22x + -22x

Combine like terms: 22x + -22x = 0
-8 + -20x + 3x2 = 0

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

Divide each side by '3'.
-2.666666667 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -6.666666667x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -6.666666667x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + 2.666666667
-6.666666667x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-6.666666667x + x2 = 2.666666667

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 2.666666667 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 2.666666667 + 11.11111112

Combine like terms: 2.666666667 + 11.11111112 = 13.777777787
11.11111112 + -6.666666667x + x2 = 13.777777787

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 13.777777787

Calculate the square root of the right side: 3.71184291

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 3.71184291 and -3.71184291.


Subproblem 1
x + -3.333333334 = 3.71184291

Simplifying
x + -3.333333334 = 3.71184291

Reorder the terms:
-3.333333334 + x = 3.71184291

Solving
-3.333333334 + x = 3.71184291

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 3.71184291 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 3.71184291 + 3.333333334
x = 3.71184291 + 3.333333334

Combine like terms: 3.71184291 + 3.333333334 = 7.045176244
x = 7.045176244

Simplifying
x = 7.045176244


Subproblem 2
x + -3.333333334 = -3.71184291

Simplifying
x + -3.333333334 = -3.71184291

Reorder the terms:
-3.333333334 + x = -3.71184291

Solving
-3.333333334 + x = -3.71184291

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -3.71184291 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -3.71184291 + 3.333333334
x = -3.71184291 + 3.333333334

Combine like terms: -3.71184291 + 3.333333334 = -0.378509576
x = -0.378509576

Simplifying
x = -0.378509576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.045176244, -0.378509576}

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