2x(4-3x)=2-5x+x

Solution for 2x(4-3x)=2-5x+x equation:

Simplifying
2x(4 + -3x) = 2 + -5x + x
(4 * 2x + -3x * 2x) = 2 + -5x + x
(8x + -6x2) = 2 + -5x + x

Combine like terms: -5x + x = -4x
8x + -6x2 = 2 + -4x

Solving
8x + -6x2 = 2 + -4x

Solving for variable 'x'.

Reorder the terms:
-2 + 8x + 4x + -6x2 = 2 + -4x + -2 + 4x

Combine like terms: 8x + 4x = 12x
-2 + 12x + -6x2 = 2 + -4x + -2 + 4x

Reorder the terms:
-2 + 12x + -6x2 = 2 + -2 + -4x + 4x

Combine like terms: 2 + -2 = 0
-2 + 12x + -6x2 = 0 + -4x + 4x
-2 + 12x + -6x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-2 + 12x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 6x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 6x + -3x2)' equal to zero and attempt to solve:

Simplifying
-1 + 6x + -3x2 = 0

Solving
-1 + 6x + -3x2 = 0

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

Divide each side by '-3'.
0.3333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -2x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -2x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.3333333333
-2x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-2x + x2 = -0.3333333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.3333333333 + 1

Reorder the terms:
1 + -2x + x2 = -0.3333333333 + 1

Combine like terms: -0.3333333333 + 1 = 0.6666666667
1 + -2x + x2 = 0.6666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.6666666667

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(x + -1) equal to 0.816496581 and -0.816496581.

Subproblem 1
x + -1 = 0.816496581

Simplifying
x + -1 = 0.816496581

Reorder the terms:
-1 + x = 0.816496581

Solving
-1 + x = 0.816496581

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.816496581 + 1
x = 0.816496581 + 1

Combine like terms: 0.816496581 + 1 = 1.816496581
x = 1.816496581

Simplifying
x = 1.816496581

Subproblem 2
x + -1 = -0.816496581

Simplifying
x + -1 = -0.816496581

Reorder the terms:
-1 + x = -0.816496581

Solving
-1 + x = -0.816496581

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.816496581 + 1
x = -0.816496581 + 1

Combine like terms: -0.816496581 + 1 = 0.183503419
x = 0.183503419

Simplifying
x = 0.183503419

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.816496581, 0.183503419}
Solution
x = {1.816496581, 0.183503419}