(2.86)(0.2-x)(2.8-x)=(x)(2+x)

Solution for (2.86)(0.2-x)(2.8-x)=(x)(2+x) equation:

Simplifying
(2.86)(0.2 + -1x)(2.8 + -1x) = (x)(2 + x)

Multiply (0.2 + -1x) * (2.8 + -1x)
2.86(0.2(2.8 + -1x) + -1x * (2.8 + -1x)) = (x)(2 + x)
2.86((2.8 * 0.2 + -1x * 0.2) + -1x * (2.8 + -1x)) = (x)(2 + x)
2.86((0.56 + -0.2x) + -1x * (2.8 + -1x)) = (x)(2 + x)
2.86(0.56 + -0.2x + (2.8 * -1x + -1x * -1x)) = (x)(2 + x)
2.86(0.56 + -0.2x + (-2.8x + 1x2)) = (x)(2 + x)

Combine like terms: -0.2x + -2.8x = -3x
2.86(0.56 + -3x + 1x2) = (x)(2 + x)
(0.56 * 2.86 + -3x * 2.86 + 1x2 * 2.86) = (x)(2 + x)
(1.6016 + -8.58x + 2.86x2) = (x)(2 + x)
1.6016 + -8.58x + 2.86x2 = (2 * x + x * x)
1.6016 + -8.58x + 2.86x2 = (2x + x2)

Solving
1.6016 + -8.58x + 2.86x2 = 2x + x2

Solving for variable 'x'.

Reorder the terms:
1.6016 + -8.58x + -2x + 2.86x2 + -1x2 = 2x + x2 + -2x + -1x2

Combine like terms: -8.58x + -2x = -10.58x
1.6016 + -10.58x + 2.86x2 + -1x2 = 2x + x2 + -2x + -1x2

Combine like terms: 2.86x2 + -1x2 = 1.86x2
1.6016 + -10.58x + 1.86x2 = 2x + x2 + -2x + -1x2

Reorder the terms:
1.6016 + -10.58x + 1.86x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
1.6016 + -10.58x + 1.86x2 = 0 + x2 + -1x2
1.6016 + -10.58x + 1.86x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1.6016 + -10.58x + 1.86x2 = 0

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

Divide each side by '1.86'.
0.8610752688 + -5.688172043x + x2 = 0

Move the constant term to the right:

Add '-0.8610752688' to each side of the equation.
0.8610752688 + -5.688172043x + -0.8610752688 + x2 = 0 + -0.8610752688

Reorder the terms:
0.8610752688 + -0.8610752688 + -5.688172043x + x2 = 0 + -0.8610752688

Combine like terms: 0.8610752688 + -0.8610752688 = 0.0000000000
0.0000000000 + -5.688172043x + x2 = 0 + -0.8610752688
-5.688172043x + x2 = 0 + -0.8610752688

Combine like terms: 0 + -0.8610752688 = -0.8610752688
-5.688172043x + x2 = -0.8610752688

The x term is -5.688172043x.  Take half its coefficient (-2.844086022).
Square it (8.088825301) and add it to both sides.

Add '8.088825301' to each side of the equation.
-5.688172043x + 8.088825301 + x2 = -0.8610752688 + 8.088825301

Reorder the terms:
8.088825301 + -5.688172043x + x2 = -0.8610752688 + 8.088825301

Combine like terms: -0.8610752688 + 8.088825301 = 7.2277500322
8.088825301 + -5.688172043x + x2 = 7.2277500322

Factor a perfect square on the left side:
(x + -2.844086022)(x + -2.844086022) = 7.2277500322

Calculate the square root of the right side: 2.688447513

Break this problem into two subproblems by setting 
(x + -2.844086022) equal to 2.688447513 and -2.688447513.

Subproblem 1
x + -2.844086022 = 2.688447513

Simplifying
x + -2.844086022 = 2.688447513

Reorder the terms:
-2.844086022 + x = 2.688447513

Solving
-2.844086022 + x = 2.688447513

Solving for variable 'x'.

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

Add '2.844086022' to each side of the equation.
-2.844086022 + 2.844086022 + x = 2.688447513 + 2.844086022

Combine like terms: -2.844086022 + 2.844086022 = 0.000000000
0.000000000 + x = 2.688447513 + 2.844086022
x = 2.688447513 + 2.844086022

Combine like terms: 2.688447513 + 2.844086022 = 5.532533535
x = 5.532533535

Simplifying
x = 5.532533535

Subproblem 2
x + -2.844086022 = -2.688447513

Simplifying
x + -2.844086022 = -2.688447513

Reorder the terms:
-2.844086022 + x = -2.688447513

Solving
-2.844086022 + x = -2.688447513

Solving for variable 'x'.

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

Add '2.844086022' to each side of the equation.
-2.844086022 + 2.844086022 + x = -2.688447513 + 2.844086022

Combine like terms: -2.844086022 + 2.844086022 = 0.000000000
0.000000000 + x = -2.688447513 + 2.844086022
x = -2.688447513 + 2.844086022

Combine like terms: -2.688447513 + 2.844086022 = 0.155638509
x = 0.155638509

Simplifying
x = 0.155638509

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.532533535, 0.155638509}