(.102)(.215-x)(.215-x)=x

Solution for (.102)(.215-x)(.215-x)=x equation:

Simplifying
(0.102)(0.215 + -1x)(0.215 + -1x) = x

Multiply (0.215 + -1x) * (0.215 + -1x)
0.102(0.215(0.215 + -1x) + -1x * (0.215 + -1x)) = x
0.102((0.215 * 0.215 + -1x * 0.215) + -1x * (0.215 + -1x)) = x
0.102((0.046225 + -0.215x) + -1x * (0.215 + -1x)) = x
0.102(0.046225 + -0.215x + (0.215 * -1x + -1x * -1x)) = x
0.102(0.046225 + -0.215x + (-0.215x + 1x2)) = x

Combine like terms: -0.215x + -0.215x = -0.43x
0.102(0.046225 + -0.43x + 1x2) = x
(0.046225 * 0.102 + -0.43x * 0.102 + 1x2 * 0.102) = x
(0.00471495 + -0.04386x + 0.102x2) = x

Solving
0.00471495 + -0.04386x + 0.102x2 = x

Solving for variable 'x'.

Reorder the terms:
0.00471495 + -0.04386x + -1x + 0.102x2 = x + -1x

Combine like terms: -0.04386x + -1x = -1.04386x
0.00471495 + -1.04386x + 0.102x2 = x + -1x

Combine like terms: x + -1x = 0
0.00471495 + -1.04386x + 0.102x2 = 0

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

Divide each side by '0.102'.
0.046225 + -10.23392157x + x2 = 0

Move the constant term to the right:

Add '-0.046225' to each side of the equation.
0.046225 + -10.23392157x + -0.046225 + x2 = 0 + -0.046225

Reorder the terms:
0.046225 + -0.046225 + -10.23392157x + x2 = 0 + -0.046225

Combine like terms: 0.046225 + -0.046225 = 0.000000
0.000000 + -10.23392157x + x2 = 0 + -0.046225
-10.23392157x + x2 = 0 + -0.046225

Combine like terms: 0 + -0.046225 = -0.046225
-10.23392157x + x2 = -0.046225

The x term is -10.23392157x.  Take half its coefficient (-5.116960785).
Square it (26.18328768) and add it to both sides.

Add '26.18328768' to each side of the equation.
-10.23392157x + 26.18328768 + x2 = -0.046225 + 26.18328768

Reorder the terms:
26.18328768 + -10.23392157x + x2 = -0.046225 + 26.18328768

Combine like terms: -0.046225 + 26.18328768 = 26.13706268
26.18328768 + -10.23392157x + x2 = 26.13706268

Factor a perfect square on the left side:
(x + -5.116960785)(x + -5.116960785) = 26.13706268

Calculate the square root of the right side: 5.112441949

Break this problem into two subproblems by setting 
(x + -5.116960785) equal to 5.112441949 and -5.112441949.

Subproblem 1
x + -5.116960785 = 5.112441949

Simplifying
x + -5.116960785 = 5.112441949

Reorder the terms:
-5.116960785 + x = 5.112441949

Solving
-5.116960785 + x = 5.112441949

Solving for variable 'x'.

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

Add '5.116960785' to each side of the equation.
-5.116960785 + 5.116960785 + x = 5.112441949 + 5.116960785

Combine like terms: -5.116960785 + 5.116960785 = 0.000000000
0.000000000 + x = 5.112441949 + 5.116960785
x = 5.112441949 + 5.116960785

Combine like terms: 5.112441949 + 5.116960785 = 10.229402734
x = 10.229402734

Simplifying
x = 10.229402734

Subproblem 2
x + -5.116960785 = -5.112441949

Simplifying
x + -5.116960785 = -5.112441949

Reorder the terms:
-5.116960785 + x = -5.112441949

Solving
-5.116960785 + x = -5.112441949

Solving for variable 'x'.

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

Add '5.116960785' to each side of the equation.
-5.116960785 + 5.116960785 + x = -5.112441949 + 5.116960785

Combine like terms: -5.116960785 + 5.116960785 = 0.000000000
0.000000000 + x = -5.112441949 + 5.116960785
x = -5.112441949 + 5.116960785

Combine like terms: -5.112441949 + 5.116960785 = 0.004518836
x = 0.004518836

Simplifying
x = 0.004518836

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.229402734, 0.004518836}