x(2-3)+4x=10x(x-4)+6

Solution for x(2-3)+4x=10x(x-4)+6 equation:

Simplifying
x(2 + -3) + 4x = 10x(x + -4) + 6

Combine like terms: 2 + -3 = -1
x(-1) + 4x = 10x(x + -4) + 6

Reorder the terms for easier multiplication:
-1x + 4x = 10x(x + -4) + 6

Combine like terms: -1x + 4x = 3x
3x = 10x(x + -4) + 6

Reorder the terms:
3x = 10x(-4 + x) + 6
3x = (-4 * 10x + x * 10x) + 6
3x = (-40x + 10x2) + 6

Reorder the terms:
3x = 6 + -40x + 10x2

Solving
3x = 6 + -40x + 10x2

Solving for variable 'x'.

Reorder the terms:
-6 + 3x + 40x + -10x2 = 6 + -40x + 10x2 + -6 + 40x + -10x2

Combine like terms: 3x + 40x = 43x
-6 + 43x + -10x2 = 6 + -40x + 10x2 + -6 + 40x + -10x2

Reorder the terms:
-6 + 43x + -10x2 = 6 + -6 + -40x + 40x + 10x2 + -10x2

Combine like terms: 6 + -6 = 0
-6 + 43x + -10x2 = 0 + -40x + 40x + 10x2 + -10x2
-6 + 43x + -10x2 = -40x + 40x + 10x2 + -10x2

Combine like terms: -40x + 40x = 0
-6 + 43x + -10x2 = 0 + 10x2 + -10x2
-6 + 43x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-6 + 43x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
0.6 + -4.3x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -4.3x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -4.3x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -4.3x + x2 = 0 + -0.6
-4.3x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-4.3x + x2 = -0.6

The x term is -4.3x.  Take half its coefficient (-2.15).
Square it (4.6225) and add it to both sides.

Add '4.6225' to each side of the equation.
-4.3x + 4.6225 + x2 = -0.6 + 4.6225

Reorder the terms:
4.6225 + -4.3x + x2 = -0.6 + 4.6225

Combine like terms: -0.6 + 4.6225 = 4.0225
4.6225 + -4.3x + x2 = 4.0225

Factor a perfect square on the left side:
(x + -2.15)(x + -2.15) = 4.0225

Calculate the square root of the right side: 2.005617112

Break this problem into two subproblems by setting 
(x + -2.15) equal to 2.005617112 and -2.005617112.

Subproblem 1
x + -2.15 = 2.005617112

Simplifying
x + -2.15 = 2.005617112

Reorder the terms:
-2.15 + x = 2.005617112

Solving
-2.15 + x = 2.005617112

Solving for variable 'x'.

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

Add '2.15' to each side of the equation.
-2.15 + 2.15 + x = 2.005617112 + 2.15

Combine like terms: -2.15 + 2.15 = 0.00
0.00 + x = 2.005617112 + 2.15
x = 2.005617112 + 2.15

Combine like terms: 2.005617112 + 2.15 = 4.155617112
x = 4.155617112

Simplifying
x = 4.155617112

Subproblem 2
x + -2.15 = -2.005617112

Simplifying
x + -2.15 = -2.005617112

Reorder the terms:
-2.15 + x = -2.005617112

Solving
-2.15 + x = -2.005617112

Solving for variable 'x'.

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

Add '2.15' to each side of the equation.
-2.15 + 2.15 + x = -2.005617112 + 2.15

Combine like terms: -2.15 + 2.15 = 0.00
0.00 + x = -2.005617112 + 2.15
x = -2.005617112 + 2.15

Combine like terms: -2.005617112 + 2.15 = 0.144382888
x = 0.144382888

Simplifying
x = 0.144382888

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.155617112, 0.144382888}