0.4x-0.8x(9-3x)=-0.6(x-5)

Solution for 0.4x-0.8x(9-3x)=-0.6(x-5) equation:

Simplifying
0.4x + -0.8x(9 + -3x) = -0.6(x + -5)
0.4x + (9 * -0.8x + -3x * -0.8x) = -0.6(x + -5)
0.4x + (-7.2x + 2.4x2) = -0.6(x + -5)

Combine like terms: 0.4x + -7.2x = -6.8x
-6.8x + 2.4x2 = -0.6(x + -5)

Reorder the terms:
-6.8x + 2.4x2 = -0.6(-5 + x)
-6.8x + 2.4x2 = (-5 * -0.6 + x * -0.6)
-6.8x + 2.4x2 = (3 + -0.6x)

Solving
-6.8x + 2.4x2 = 3 + -0.6x

Solving for variable 'x'.

Reorder the terms:
-3 + -6.8x + 0.6x + 2.4x2 = 3 + -0.6x + -3 + 0.6x

Combine like terms: -6.8x + 0.6x = -6.2x
-3 + -6.2x + 2.4x2 = 3 + -0.6x + -3 + 0.6x

Reorder the terms:
-3 + -6.2x + 2.4x2 = 3 + -3 + -0.6x + 0.6x

Combine like terms: 3 + -3 = 0
-3 + -6.2x + 2.4x2 = 0 + -0.6x + 0.6x
-3 + -6.2x + 2.4x2 = -0.6x + 0.6x

Combine like terms: -0.6x + 0.6x = 0.0
-3 + -6.2x + 2.4x2 = 0.0

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

Divide each side by '2.4'.
-1.25 + -2.583333333x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -2.583333333x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -2.583333333x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -2.583333333x + x2 = 0 + 1.25
-2.583333333x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-2.583333333x + x2 = 1.25

The x term is -2.583333333x.  Take half its coefficient (-1.291666667).
Square it (1.668402779) and add it to both sides.

Add '1.668402779' to each side of the equation.
-2.583333333x + 1.668402779 + x2 = 1.25 + 1.668402779

Reorder the terms:
1.668402779 + -2.583333333x + x2 = 1.25 + 1.668402779

Combine like terms: 1.25 + 1.668402779 = 2.918402779
1.668402779 + -2.583333333x + x2 = 2.918402779

Factor a perfect square on the left side:
(x + -1.291666667)(x + -1.291666667) = 2.918402779

Calculate the square root of the right side: 1.708333334

Break this problem into two subproblems by setting 
(x + -1.291666667) equal to 1.708333334 and -1.708333334.

Subproblem 1
x + -1.291666667 = 1.708333334

Simplifying
x + -1.291666667 = 1.708333334

Reorder the terms:
-1.291666667 + x = 1.708333334

Solving
-1.291666667 + x = 1.708333334

Solving for variable 'x'.

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

Add '1.291666667' to each side of the equation.
-1.291666667 + 1.291666667 + x = 1.708333334 + 1.291666667

Combine like terms: -1.291666667 + 1.291666667 = 0.000000000
0.000000000 + x = 1.708333334 + 1.291666667
x = 1.708333334 + 1.291666667

Combine like terms: 1.708333334 + 1.291666667 = 3.000000001
x = 3.000000001

Simplifying
x = 3.000000001

Subproblem 2
x + -1.291666667 = -1.708333334

Simplifying
x + -1.291666667 = -1.708333334

Reorder the terms:
-1.291666667 + x = -1.708333334

Solving
-1.291666667 + x = -1.708333334

Solving for variable 'x'.

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

Add '1.291666667' to each side of the equation.
-1.291666667 + 1.291666667 + x = -1.708333334 + 1.291666667

Combine like terms: -1.291666667 + 1.291666667 = 0.000000000
0.000000000 + x = -1.708333334 + 1.291666667
x = -1.708333334 + 1.291666667

Combine like terms: -1.708333334 + 1.291666667 = -0.416666667
x = -0.416666667

Simplifying
x = -0.416666667

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.000000001, -0.416666667}