x(2x-4)-3x(x^2+4x-8)=

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


Simplifying
x(2x + -4) + -3x(x2 + 4x + -8) = 0

Reorder the terms:
x(-4 + 2x) + -3x(x2 + 4x + -8) = 0
(-4 * x + 2x * x) + -3x(x2 + 4x + -8) = 0
(-4x + 2x2) + -3x(x2 + 4x + -8) = 0

Reorder the terms:
-4x + 2x2 + -3x(-8 + 4x + x2) = 0
-4x + 2x2 + (-8 * -3x + 4x * -3x + x2 * -3x) = 0
-4x + 2x2 + (24x + -12x2 + -3x3) = 0

Reorder the terms:
-4x + 24x + 2x2 + -12x2 + -3x3 = 0

Combine like terms: -4x + 24x = 20x
20x + 2x2 + -12x2 + -3x3 = 0

Combine like terms: 2x2 + -12x2 = -10x2
20x + -10x2 + -3x3 = 0

Solving
20x + -10x2 + -3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(20 + -10x + -3x2) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(20 + -10x + -3x2)' equal to zero and attempt to solve:

Simplifying
20 + -10x + -3x2 = 0

Solving
20 + -10x + -3x2 = 0

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

Divide each side by '-3'.
-6.666666667 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 3.333333333x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 3.333333333x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + 6.666666667
3.333333333x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
3.333333333x + x2 = 6.666666667

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 6.666666667 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 6.666666667 + 2.777777779

Combine like terms: 6.666666667 + 2.777777779 = 9.444444446
2.777777779 + 3.333333333x + x2 = 9.444444446

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 9.444444446

Calculate the square root of the right side: 3.073181486

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 3.073181486 and -3.073181486.


Subproblem 1
x + 1.666666667 = 3.073181486

Simplifying
x + 1.666666667 = 3.073181486

Reorder the terms:
1.666666667 + x = 3.073181486

Solving
1.666666667 + x = 3.073181486

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 3.073181486 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 3.073181486 + -1.666666667
x = 3.073181486 + -1.666666667

Combine like terms: 3.073181486 + -1.666666667 = 1.406514819
x = 1.406514819

Simplifying
x = 1.406514819


Subproblem 2
x + 1.666666667 = -3.073181486

Simplifying
x + 1.666666667 = -3.073181486

Reorder the terms:
1.666666667 + x = -3.073181486

Solving
1.666666667 + x = -3.073181486

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -3.073181486 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -3.073181486 + -1.666666667
x = -3.073181486 + -1.666666667

Combine like terms: -3.073181486 + -1.666666667 = -4.739848153
x = -4.739848153

Simplifying
x = -4.739848153


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.406514819, -4.739848153}
Solution
x = {0, 1.406514819, -4.739848153}

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