x(6x-1)-3(6x+1)=0

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Solution for x(6x-1)-3(6x+1)=0 equation: 


Simplifying
x(6x + -1) + -3(6x + 1) = 0

Reorder the terms:
x(-1 + 6x) + -3(6x + 1) = 0
(-1 * x + 6x * x) + -3(6x + 1) = 0
(-1x + 6x2) + -3(6x + 1) = 0

Reorder the terms:
-1x + 6x2 + -3(1 + 6x) = 0
-1x + 6x2 + (1 * -3 + 6x * -3) = 0
-1x + 6x2 + (-3 + -18x) = 0

Reorder the terms:
-3 + -1x + -18x + 6x2 = 0

Combine like terms: -1x + -18x = -19x
-3 + -19x + 6x2 = 0

Solving
-3 + -19x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-0.5 + -3.166666667x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -3.166666667x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -3.166666667x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -3.166666667x + x2 = 0 + 0.5
-3.166666667x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-3.166666667x + x2 = 0.5

The x term is -3.166666667x.  Take half its coefficient (-1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
-3.166666667x + 2.506944447 + x2 = 0.5 + 2.506944447

Reorder the terms:
2.506944447 + -3.166666667x + x2 = 0.5 + 2.506944447

Combine like terms: 0.5 + 2.506944447 = 3.006944447
2.506944447 + -3.166666667x + x2 = 3.006944447

Factor a perfect square on the left side:
(x + -1.583333334)(x + -1.583333334) = 3.006944447

Calculate the square root of the right side: 1.734054338

Break this problem into two subproblems by setting 
(x + -1.583333334) equal to 1.734054338 and -1.734054338.


Subproblem 1
x + -1.583333334 = 1.734054338

Simplifying
x + -1.583333334 = 1.734054338

Reorder the terms:
-1.583333334 + x = 1.734054338

Solving
-1.583333334 + x = 1.734054338

Solving for variable 'x'.

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

Add '1.583333334' to each side of the equation.
-1.583333334 + 1.583333334 + x = 1.734054338 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + x = 1.734054338 + 1.583333334
x = 1.734054338 + 1.583333334

Combine like terms: 1.734054338 + 1.583333334 = 3.317387672
x = 3.317387672

Simplifying
x = 3.317387672


Subproblem 2
x + -1.583333334 = -1.734054338

Simplifying
x + -1.583333334 = -1.734054338

Reorder the terms:
-1.583333334 + x = -1.734054338

Solving
-1.583333334 + x = -1.734054338

Solving for variable 'x'.

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

Add '1.583333334' to each side of the equation.
-1.583333334 + 1.583333334 + x = -1.734054338 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + x = -1.734054338 + 1.583333334
x = -1.734054338 + 1.583333334

Combine like terms: -1.734054338 + 1.583333334 = -0.150721004
x = -0.150721004

Simplifying
x = -0.150721004


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.317387672, -0.150721004}

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