-0.2x(x-6)+x=0.3(4-x)

Solution for -0.2x(x-6)+x=0.3(4-x) equation:

Simplifying
-0.2x(x + -6) + x = 0.3(4 + -1x)

Reorder the terms:
-0.2x(-6 + x) + x = 0.3(4 + -1x)
(-6 * -0.2x + x * -0.2x) + x = 0.3(4 + -1x)
(1.2x + -0.2x2) + x = 0.3(4 + -1x)

Reorder the terms:
1.2x + x + -0.2x2 = 0.3(4 + -1x)

Combine like terms: 1.2x + x = 2.2x
2.2x + -0.2x2 = 0.3(4 + -1x)
2.2x + -0.2x2 = (4 * 0.3 + -1x * 0.3)
2.2x + -0.2x2 = (1.2 + -0.3x)

Solving
2.2x + -0.2x2 = 1.2 + -0.3x

Solving for variable 'x'.

Reorder the terms:
-1.2 + 2.2x + 0.3x + -0.2x2 = 1.2 + -0.3x + -1.2 + 0.3x

Combine like terms: 2.2x + 0.3x = 2.5x
-1.2 + 2.5x + -0.2x2 = 1.2 + -0.3x + -1.2 + 0.3x

Reorder the terms:
-1.2 + 2.5x + -0.2x2 = 1.2 + -1.2 + -0.3x + 0.3x

Combine like terms: 1.2 + -1.2 = 0.0
-1.2 + 2.5x + -0.2x2 = 0.0 + -0.3x + 0.3x
-1.2 + 2.5x + -0.2x2 = -0.3x + 0.3x

Combine like terms: -0.3x + 0.3x = 0.0
-1.2 + 2.5x + -0.2x2 = 0.0

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
6 + -12.5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -12.5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -12.5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -12.5x + x2 = 0 + -6
-12.5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-12.5x + x2 = -6

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -6 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -6 + 39.0625

Combine like terms: -6 + 39.0625 = 33.0625
39.0625 + -12.5x + x2 = 33.0625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 33.0625

Calculate the square root of the right side: 5.75

Break this problem into two subproblems by setting 
(x + -6.25) equal to 5.75 and -5.75.

Subproblem 1
x + -6.25 = 5.75

Simplifying
x + -6.25 = 5.75

Reorder the terms:
-6.25 + x = 5.75

Solving
-6.25 + x = 5.75

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 5.75 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 5.75 + 6.25
x = 5.75 + 6.25

Combine like terms: 5.75 + 6.25 = 12
x = 12

Simplifying
x = 12

Subproblem 2
x + -6.25 = -5.75

Simplifying
x + -6.25 = -5.75

Reorder the terms:
-6.25 + x = -5.75

Solving
-6.25 + x = -5.75

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -5.75 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -5.75 + 6.25
x = -5.75 + 6.25

Combine like terms: -5.75 + 6.25 = 0.5
x = 0.5

Simplifying
x = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12, 0.5}