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

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


Simplifying
-4(2 + -3x) = 2(3x + -8) * 2x
(2 * -4 + -3x * -4) = 2(3x + -8) * 2x
(-8 + 12x) = 2(3x + -8) * 2x

Reorder the terms:
-8 + 12x = 2(-8 + 3x) * 2x

Reorder the terms for easier multiplication:
-8 + 12x = 2 * 2x(-8 + 3x)

Multiply 2 * 2
-8 + 12x = 4x(-8 + 3x)
-8 + 12x = (-8 * 4x + 3x * 4x)
-8 + 12x = (-32x + 12x2)

Solving
-8 + 12x = -32x + 12x2

Solving for variable 'x'.

Combine like terms: 12x + 32x = 44x
-8 + 44x + -12x2 = -32x + 12x2 + 32x + -12x2

Reorder the terms:
-8 + 44x + -12x2 = -32x + 32x + 12x2 + -12x2

Combine like terms: -32x + 32x = 0
-8 + 44x + -12x2 = 0 + 12x2 + -12x2
-8 + 44x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-8 + 44x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 11x + -3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + 11x + -3x2)' equal to zero and attempt to solve:

Simplifying
-2 + 11x + -3x2 = 0

Solving
-2 + 11x + -3x2 = 0

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

Divide each side by '-3'.
0.6666666667 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -3.666666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -3.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -3.666666667x + x2 = 0 + -0.6666666667
-3.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-3.666666667x + x2 = -0.6666666667

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = -0.6666666667 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = -0.6666666667 + 3.361111114

Combine like terms: -0.6666666667 + 3.361111114 = 2.6944444473
3.361111114 + -3.666666667x + x2 = 2.6944444473

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 2.6944444473

Calculate the square root of the right side: 1.641476301

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 1.641476301 and -1.641476301.


Subproblem 1
x + -1.833333334 = 1.641476301

Simplifying
x + -1.833333334 = 1.641476301

Reorder the terms:
-1.833333334 + x = 1.641476301

Solving
-1.833333334 + x = 1.641476301

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 1.641476301 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 1.641476301 + 1.833333334
x = 1.641476301 + 1.833333334

Combine like terms: 1.641476301 + 1.833333334 = 3.474809635
x = 3.474809635

Simplifying
x = 3.474809635


Subproblem 2
x + -1.833333334 = -1.641476301

Simplifying
x + -1.833333334 = -1.641476301

Reorder the terms:
-1.833333334 + x = -1.641476301

Solving
-1.833333334 + x = -1.641476301

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -1.641476301 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -1.641476301 + 1.833333334
x = -1.641476301 + 1.833333334

Combine like terms: -1.641476301 + 1.833333334 = 0.191857033
x = 0.191857033

Simplifying
x = 0.191857033


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.474809635, 0.191857033}
Solution
x = {3.474809635, 0.191857033}

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