3.1(x+2)-1.5x=5.2x(x-4)

Solution for 3.1(x+2)-1.5x=5.2x(x-4) equation:

Simplifying
3.1(x + 2) + -1.5x = 5.2x(x + -4)

Reorder the terms:
3.1(2 + x) + -1.5x = 5.2x(x + -4)
(2 * 3.1 + x * 3.1) + -1.5x = 5.2x(x + -4)
(6.2 + 3.1x) + -1.5x = 5.2x(x + -4)

Combine like terms: 3.1x + -1.5x = 1.6x
6.2 + 1.6x = 5.2x(x + -4)

Reorder the terms:
6.2 + 1.6x = 5.2x(-4 + x)
6.2 + 1.6x = (-4 * 5.2x + x * 5.2x)
6.2 + 1.6x = (-20.8x + 5.2x2)

Solving
6.2 + 1.6x = -20.8x + 5.2x2

Solving for variable 'x'.

Combine like terms: 1.6x + 20.8x = 22.4x
6.2 + 22.4x + -5.2x2 = -20.8x + 5.2x2 + 20.8x + -5.2x2

Reorder the terms:
6.2 + 22.4x + -5.2x2 = -20.8x + 20.8x + 5.2x2 + -5.2x2

Combine like terms: -20.8x + 20.8x = 0.0
6.2 + 22.4x + -5.2x2 = 0.0 + 5.2x2 + -5.2x2
6.2 + 22.4x + -5.2x2 = 5.2x2 + -5.2x2

Combine like terms: 5.2x2 + -5.2x2 = 0.0
6.2 + 22.4x + -5.2x2 = 0.0

Begin completing the square.  Divide all terms by
-5.2 the coefficient of the squared term: 

Divide each side by '-5.2'.
-1.192307692 + -4.307692308x + x2 = 0

Move the constant term to the right:

Add '1.192307692' to each side of the equation.
-1.192307692 + -4.307692308x + 1.192307692 + x2 = 0 + 1.192307692

Reorder the terms:
-1.192307692 + 1.192307692 + -4.307692308x + x2 = 0 + 1.192307692

Combine like terms: -1.192307692 + 1.192307692 = 0.000000000
0.000000000 + -4.307692308x + x2 = 0 + 1.192307692
-4.307692308x + x2 = 0 + 1.192307692

Combine like terms: 0 + 1.192307692 = 1.192307692
-4.307692308x + x2 = 1.192307692

The x term is -4.307692308x.  Take half its coefficient (-2.153846154).
Square it (4.639053255) and add it to both sides.

Add '4.639053255' to each side of the equation.
-4.307692308x + 4.639053255 + x2 = 1.192307692 + 4.639053255

Reorder the terms:
4.639053255 + -4.307692308x + x2 = 1.192307692 + 4.639053255

Combine like terms: 1.192307692 + 4.639053255 = 5.831360947
4.639053255 + -4.307692308x + x2 = 5.831360947

Factor a perfect square on the left side:
(x + -2.153846154)(x + -2.153846154) = 5.831360947

Calculate the square root of the right side: 2.4148211

Break this problem into two subproblems by setting 
(x + -2.153846154) equal to 2.4148211 and -2.4148211.

Subproblem 1
x + -2.153846154 = 2.4148211

Simplifying
x + -2.153846154 = 2.4148211

Reorder the terms:
-2.153846154 + x = 2.4148211

Solving
-2.153846154 + x = 2.4148211

Solving for variable 'x'.

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

Add '2.153846154' to each side of the equation.
-2.153846154 + 2.153846154 + x = 2.4148211 + 2.153846154

Combine like terms: -2.153846154 + 2.153846154 = 0.000000000
0.000000000 + x = 2.4148211 + 2.153846154
x = 2.4148211 + 2.153846154

Combine like terms: 2.4148211 + 2.153846154 = 4.568667254
x = 4.568667254

Simplifying
x = 4.568667254

Subproblem 2
x + -2.153846154 = -2.4148211

Simplifying
x + -2.153846154 = -2.4148211

Reorder the terms:
-2.153846154 + x = -2.4148211

Solving
-2.153846154 + x = -2.4148211

Solving for variable 'x'.

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

Add '2.153846154' to each side of the equation.
-2.153846154 + 2.153846154 + x = -2.4148211 + 2.153846154

Combine like terms: -2.153846154 + 2.153846154 = 0.000000000
0.000000000 + x = -2.4148211 + 2.153846154
x = -2.4148211 + 2.153846154

Combine like terms: -2.4148211 + 2.153846154 = -0.260974946
x = -0.260974946

Simplifying
x = -0.260974946

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.568667254, -0.260974946}