(0.8+x)(3.6+x)=0.113(1.4-x)(-x)

Solution for (0.8+x)(3.6+x)=0.113(1.4-x)(-x) equation:

Simplifying
(0.8 + x)(3.6 + x) = 0.113(1.4 + -1x)(-1x)

Multiply (0.8 + x) * (3.6 + x)
(0.8(3.6 + x) + x(3.6 + x)) = 0.113(1.4 + -1x)(-1x)
((3.6 * 0.8 + x * 0.8) + x(3.6 + x)) = 0.113(1.4 + -1x)(-1x)
((2.88 + 0.8x) + x(3.6 + x)) = 0.113(1.4 + -1x)(-1x)
(2.88 + 0.8x + (3.6 * x + x * x)) = 0.113(1.4 + -1x)(-1x)
(2.88 + 0.8x + (3.6x + x2)) = 0.113(1.4 + -1x)(-1x)

Combine like terms: 0.8x + 3.6x = 4.4x
(2.88 + 4.4x + x2) = 0.113(1.4 + -1x)(-1x)

Remove parenthesis around (-1x)
2.88 + 4.4x + x2 = 0.113(1.4 + -1x) * -1x

Reorder the terms for easier multiplication:
2.88 + 4.4x + x2 = 0.113 * -1x(1.4 + -1x)

Multiply 0.113 * -1
2.88 + 4.4x + x2 = -0.113x(1.4 + -1x)
2.88 + 4.4x + x2 = (1.4 * -0.113x + -1x * -0.113x)
2.88 + 4.4x + x2 = (-0.1582x + 0.113x2)

Solving
2.88 + 4.4x + x2 = -0.1582x + 0.113x2

Solving for variable 'x'.

Reorder the terms:
2.88 + 4.4x + 0.1582x + x2 + -0.113x2 = -0.1582x + 0.113x2 + 0.1582x + -0.113x2

Combine like terms: 4.4x + 0.1582x = 4.5582x
2.88 + 4.5582x + x2 + -0.113x2 = -0.1582x + 0.113x2 + 0.1582x + -0.113x2

Combine like terms: x2 + -0.113x2 = 0.887x2
2.88 + 4.5582x + 0.887x2 = -0.1582x + 0.113x2 + 0.1582x + -0.113x2

Reorder the terms:
2.88 + 4.5582x + 0.887x2 = -0.1582x + 0.1582x + 0.113x2 + -0.113x2

Combine like terms: -0.1582x + 0.1582x = 0.0000
2.88 + 4.5582x + 0.887x2 = 0.0000 + 0.113x2 + -0.113x2
2.88 + 4.5582x + 0.887x2 = 0.113x2 + -0.113x2

Combine like terms: 0.113x2 + -0.113x2 = 0.000
2.88 + 4.5582x + 0.887x2 = 0.000

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

Divide each side by '0.887'.
3.246899662 + 5.138895152x + x2 = 0

Move the constant term to the right:

Add '-3.246899662' to each side of the equation.
3.246899662 + 5.138895152x + -3.246899662 + x2 = 0 + -3.246899662

Reorder the terms:
3.246899662 + -3.246899662 + 5.138895152x + x2 = 0 + -3.246899662

Combine like terms: 3.246899662 + -3.246899662 = 0.000000000
0.000000000 + 5.138895152x + x2 = 0 + -3.246899662
5.138895152x + x2 = 0 + -3.246899662

Combine like terms: 0 + -3.246899662 = -3.246899662
5.138895152x + x2 = -3.246899662

The x term is 5.138895152x.  Take half its coefficient (2.569447576).
Square it (6.602060846) and add it to both sides.

Add '6.602060846' to each side of the equation.
5.138895152x + 6.602060846 + x2 = -3.246899662 + 6.602060846

Reorder the terms:
6.602060846 + 5.138895152x + x2 = -3.246899662 + 6.602060846

Combine like terms: -3.246899662 + 6.602060846 = 3.355161184
6.602060846 + 5.138895152x + x2 = 3.355161184

Factor a perfect square on the left side:
(x + 2.569447576)(x + 2.569447576) = 3.355161184

Calculate the square root of the right side: 1.831709907

Break this problem into two subproblems by setting 
(x + 2.569447576) equal to 1.831709907 and -1.831709907.

Subproblem 1
x + 2.569447576 = 1.831709907

Simplifying
x + 2.569447576 = 1.831709907

Reorder the terms:
2.569447576 + x = 1.831709907

Solving
2.569447576 + x = 1.831709907

Solving for variable 'x'.

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

Add '-2.569447576' to each side of the equation.
2.569447576 + -2.569447576 + x = 1.831709907 + -2.569447576

Combine like terms: 2.569447576 + -2.569447576 = 0.000000000
0.000000000 + x = 1.831709907 + -2.569447576
x = 1.831709907 + -2.569447576

Combine like terms: 1.831709907 + -2.569447576 = -0.737737669
x = -0.737737669

Simplifying
x = -0.737737669

Subproblem 2
x + 2.569447576 = -1.831709907

Simplifying
x + 2.569447576 = -1.831709907

Reorder the terms:
2.569447576 + x = -1.831709907

Solving
2.569447576 + x = -1.831709907

Solving for variable 'x'.

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

Add '-2.569447576' to each side of the equation.
2.569447576 + -2.569447576 + x = -1.831709907 + -2.569447576

Combine like terms: 2.569447576 + -2.569447576 = 0.000000000
0.000000000 + x = -1.831709907 + -2.569447576
x = -1.831709907 + -2.569447576

Combine like terms: -1.831709907 + -2.569447576 = -4.401157483
x = -4.401157483

Simplifying
x = -4.401157483

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.737737669, -4.401157483}