52x(14-13x)-6=43+4x

Solution for 52x(14-13x)-6=43+4x equation:

Simplifying
52x(14 + -13x) + -6 = 43 + 4x
(14 * 52x + -13x * 52x) + -6 = 43 + 4x
(728x + -676x2) + -6 = 43 + 4x

Reorder the terms:
-6 + 728x + -676x2 = 43 + 4x

Solving
-6 + 728x + -676x2 = 43 + 4x

Solving for variable 'x'.

Reorder the terms:
-6 + -43 + 728x + -4x + -676x2 = 43 + 4x + -43 + -4x

Combine like terms: -6 + -43 = -49
-49 + 728x + -4x + -676x2 = 43 + 4x + -43 + -4x

Combine like terms: 728x + -4x = 724x
-49 + 724x + -676x2 = 43 + 4x + -43 + -4x

Reorder the terms:
-49 + 724x + -676x2 = 43 + -43 + 4x + -4x

Combine like terms: 43 + -43 = 0
-49 + 724x + -676x2 = 0 + 4x + -4x
-49 + 724x + -676x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-49 + 724x + -676x2 = 0

Begin completing the square.  Divide all terms by
-676 the coefficient of the squared term: 

Divide each side by '-676'.
0.0724852071 + -1.071005917x + x2 = 0

Move the constant term to the right:

Add '-0.0724852071' to each side of the equation.
0.0724852071 + -1.071005917x + -0.0724852071 + x2 = 0 + -0.0724852071

Reorder the terms:
0.0724852071 + -0.0724852071 + -1.071005917x + x2 = 0 + -0.0724852071

Combine like terms: 0.0724852071 + -0.0724852071 = 0.0000000000
0.0000000000 + -1.071005917x + x2 = 0 + -0.0724852071
-1.071005917x + x2 = 0 + -0.0724852071

Combine like terms: 0 + -0.0724852071 = -0.0724852071
-1.071005917x + x2 = -0.0724852071

The x term is -1.071005917x.  Take half its coefficient (-0.5355029585).
Square it (0.2867634186) and add it to both sides.

Add '0.2867634186' to each side of the equation.
-1.071005917x + 0.2867634186 + x2 = -0.0724852071 + 0.2867634186

Reorder the terms:
0.2867634186 + -1.071005917x + x2 = -0.0724852071 + 0.2867634186

Combine like terms: -0.0724852071 + 0.2867634186 = 0.2142782115
0.2867634186 + -1.071005917x + x2 = 0.2142782115

Factor a perfect square on the left side:
(x + -0.5355029585)(x + -0.5355029585) = 0.2142782115

Calculate the square root of the right side: 0.462901946

Break this problem into two subproblems by setting 
(x + -0.5355029585) equal to 0.462901946 and -0.462901946.

Subproblem 1
x + -0.5355029585 = 0.462901946

Simplifying
x + -0.5355029585 = 0.462901946

Reorder the terms:
-0.5355029585 + x = 0.462901946

Solving
-0.5355029585 + x = 0.462901946

Solving for variable 'x'.

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

Add '0.5355029585' to each side of the equation.
-0.5355029585 + 0.5355029585 + x = 0.462901946 + 0.5355029585

Combine like terms: -0.5355029585 + 0.5355029585 = 0.0000000000
0.0000000000 + x = 0.462901946 + 0.5355029585
x = 0.462901946 + 0.5355029585

Combine like terms: 0.462901946 + 0.5355029585 = 0.9984049045
x = 0.9984049045

Simplifying
x = 0.9984049045

Subproblem 2
x + -0.5355029585 = -0.462901946

Simplifying
x + -0.5355029585 = -0.462901946

Reorder the terms:
-0.5355029585 + x = -0.462901946

Solving
-0.5355029585 + x = -0.462901946

Solving for variable 'x'.

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

Add '0.5355029585' to each side of the equation.
-0.5355029585 + 0.5355029585 + x = -0.462901946 + 0.5355029585

Combine like terms: -0.5355029585 + 0.5355029585 = 0.0000000000
0.0000000000 + x = -0.462901946 + 0.5355029585
x = -0.462901946 + 0.5355029585

Combine like terms: -0.462901946 + 0.5355029585 = 0.0726010125
x = 0.0726010125

Simplifying
x = 0.0726010125

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9984049045, 0.0726010125}