0.2x(x+3)-4(2x-3)=3.4

Solution for 0.2x(x+3)-4(2x-3)=3.4 equation:

Simplifying
0.2x(x + 3) + -4(2x + -3) = 3.4

Reorder the terms:
0.2x(3 + x) + -4(2x + -3) = 3.4
(3 * 0.2x + x * 0.2x) + -4(2x + -3) = 3.4
(0.6x + 0.2x2) + -4(2x + -3) = 3.4

Reorder the terms:
0.6x + 0.2x2 + -4(-3 + 2x) = 3.4
0.6x + 0.2x2 + (-3 * -4 + 2x * -4) = 3.4
0.6x + 0.2x2 + (12 + -8x) = 3.4

Reorder the terms:
12 + 0.6x + -8x + 0.2x2 = 3.4

Combine like terms: 0.6x + -8x = -7.4x
12 + -7.4x + 0.2x2 = 3.4

Solving
12 + -7.4x + 0.2x2 = 3.4

Solving for variable 'x'.

Reorder the terms:
12 + -3.4 + -7.4x + 0.2x2 = 3.4 + -3.4

Combine like terms: 12 + -3.4 = 8.6
8.6 + -7.4x + 0.2x2 = 3.4 + -3.4

Combine like terms: 3.4 + -3.4 = 0.0
8.6 + -7.4x + 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'.
43 + -37x + x2 = 0

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + -37x + -43 + x2 = 0 + -43

Reorder the terms:
43 + -43 + -37x + x2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + -37x + x2 = 0 + -43
-37x + x2 = 0 + -43

Combine like terms: 0 + -43 = -43
-37x + x2 = -43

The x term is -37x.  Take half its coefficient (-18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
-37x + 342.25 + x2 = -43 + 342.25

Reorder the terms:
342.25 + -37x + x2 = -43 + 342.25

Combine like terms: -43 + 342.25 = 299.25
342.25 + -37x + x2 = 299.25

Factor a perfect square on the left side:
(x + -18.5)(x + -18.5) = 299.25

Calculate the square root of the right side: 17.298843892

Break this problem into two subproblems by setting 
(x + -18.5) equal to 17.298843892 and -17.298843892.

Subproblem 1
x + -18.5 = 17.298843892

Simplifying
x + -18.5 = 17.298843892

Reorder the terms:
-18.5 + x = 17.298843892

Solving
-18.5 + x = 17.298843892

Solving for variable 'x'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + x = 17.298843892 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x = 17.298843892 + 18.5
x = 17.298843892 + 18.5

Combine like terms: 17.298843892 + 18.5 = 35.798843892
x = 35.798843892

Simplifying
x = 35.798843892

Subproblem 2
x + -18.5 = -17.298843892

Simplifying
x + -18.5 = -17.298843892

Reorder the terms:
-18.5 + x = -17.298843892

Solving
-18.5 + x = -17.298843892

Solving for variable 'x'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + x = -17.298843892 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x = -17.298843892 + 18.5
x = -17.298843892 + 18.5

Combine like terms: -17.298843892 + 18.5 = 1.201156108
x = 1.201156108

Simplifying
x = 1.201156108

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.798843892, 1.201156108}