(x+0.13)*.2(x+0.13)=0.4x-0.051

Solution for (x+0.13)*.2(x+0.13)=0.4x-0.051 equation:

Simplifying
(x + 0.13) * 0.2(x + 0.13) = 0.4x + -0.051

Reorder the terms:
(0.13 + x) * 0.2(x + 0.13) = 0.4x + -0.051

Reorder the terms:
(0.13 + x) * 0.2(0.13 + x) = 0.4x + -0.051

Reorder the terms for easier multiplication:
0.2(0.13 + x)(0.13 + x) = 0.4x + -0.051

Multiply (0.13 + x) * (0.13 + x)
0.2(0.13(0.13 + x) + x(0.13 + x)) = 0.4x + -0.051
0.2((0.13 * 0.13 + x * 0.13) + x(0.13 + x)) = 0.4x + -0.051
0.2((0.0169 + 0.13x) + x(0.13 + x)) = 0.4x + -0.051
0.2(0.0169 + 0.13x + (0.13 * x + x * x)) = 0.4x + -0.051
0.2(0.0169 + 0.13x + (0.13x + x2)) = 0.4x + -0.051

Combine like terms: 0.13x + 0.13x = 0.26x
0.2(0.0169 + 0.26x + x2) = 0.4x + -0.051
(0.0169 * 0.2 + 0.26x * 0.2 + x2 * 0.2) = 0.4x + -0.051
(0.00338 + 0.052x + 0.2x2) = 0.4x + -0.051

Reorder the terms:
0.00338 + 0.052x + 0.2x2 = -0.051 + 0.4x

Solving
0.00338 + 0.052x + 0.2x2 = -0.051 + 0.4x

Solving for variable 'x'.

Reorder the terms:
0.00338 + 0.051 + 0.052x + -0.4x + 0.2x2 = -0.051 + 0.4x + 0.051 + -0.4x

Combine like terms: 0.00338 + 0.051 = 0.05438
0.05438 + 0.052x + -0.4x + 0.2x2 = -0.051 + 0.4x + 0.051 + -0.4x

Combine like terms: 0.052x + -0.4x = -0.348x
0.05438 + -0.348x + 0.2x2 = -0.051 + 0.4x + 0.051 + -0.4x

Reorder the terms:
0.05438 + -0.348x + 0.2x2 = -0.051 + 0.051 + 0.4x + -0.4x

Combine like terms: -0.051 + 0.051 = 0.000
0.05438 + -0.348x + 0.2x2 = 0.000 + 0.4x + -0.4x
0.05438 + -0.348x + 0.2x2 = 0.4x + -0.4x

Combine like terms: 0.4x + -0.4x = 0.0
0.05438 + -0.348x + 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'.
0.2719 + -1.74x + x2 = 0

Move the constant term to the right:

Add '-0.2719' to each side of the equation.
0.2719 + -1.74x + -0.2719 + x2 = 0 + -0.2719

Reorder the terms:
0.2719 + -0.2719 + -1.74x + x2 = 0 + -0.2719

Combine like terms: 0.2719 + -0.2719 = 0.0000
0.0000 + -1.74x + x2 = 0 + -0.2719
-1.74x + x2 = 0 + -0.2719

Combine like terms: 0 + -0.2719 = -0.2719
-1.74x + x2 = -0.2719

The x term is -1.74x.  Take half its coefficient (-0.87).
Square it (0.7569) and add it to both sides.

Add '0.7569' to each side of the equation.
-1.74x + 0.7569 + x2 = -0.2719 + 0.7569

Reorder the terms:
0.7569 + -1.74x + x2 = -0.2719 + 0.7569

Combine like terms: -0.2719 + 0.7569 = 0.485
0.7569 + -1.74x + x2 = 0.485

Factor a perfect square on the left side:
(x + -0.87)(x + -0.87) = 0.485

Calculate the square root of the right side: 0.696419414

Break this problem into two subproblems by setting 
(x + -0.87) equal to 0.696419414 and -0.696419414.

Subproblem 1
x + -0.87 = 0.696419414

Simplifying
x + -0.87 = 0.696419414

Reorder the terms:
-0.87 + x = 0.696419414

Solving
-0.87 + x = 0.696419414

Solving for variable 'x'.

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

Add '0.87' to each side of the equation.
-0.87 + 0.87 + x = 0.696419414 + 0.87

Combine like terms: -0.87 + 0.87 = 0.00
0.00 + x = 0.696419414 + 0.87
x = 0.696419414 + 0.87

Combine like terms: 0.696419414 + 0.87 = 1.566419414
x = 1.566419414

Simplifying
x = 1.566419414

Subproblem 2
x + -0.87 = -0.696419414

Simplifying
x + -0.87 = -0.696419414

Reorder the terms:
-0.87 + x = -0.696419414

Solving
-0.87 + x = -0.696419414

Solving for variable 'x'.

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

Add '0.87' to each side of the equation.
-0.87 + 0.87 + x = -0.696419414 + 0.87

Combine like terms: -0.87 + 0.87 = 0.00
0.00 + x = -0.696419414 + 0.87
x = -0.696419414 + 0.87

Combine like terms: -0.696419414 + 0.87 = 0.173580586
x = 0.173580586

Simplifying
x = 0.173580586

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.566419414, 0.173580586}