(6x^2-5x+3)-6(4x^2+7x-7)-(x^2-4x+2)=0

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Solution for (6x^2-5x+3)-6(4x^2+7x-7)-(x^2-4x+2)=0 equation: 


Simplifying
(6x2 + -5x + 3) + -6(4x2 + 7x + -7) + -1(x2 + -4x + 2) = 0

Reorder the terms:
(3 + -5x + 6x2) + -6(4x2 + 7x + -7) + -1(x2 + -4x + 2) = 0

Remove parenthesis around (3 + -5x + 6x2)
3 + -5x + 6x2 + -6(4x2 + 7x + -7) + -1(x2 + -4x + 2) = 0

Reorder the terms:
3 + -5x + 6x2 + -6(-7 + 7x + 4x2) + -1(x2 + -4x + 2) = 0
3 + -5x + 6x2 + (-7 * -6 + 7x * -6 + 4x2 * -6) + -1(x2 + -4x + 2) = 0
3 + -5x + 6x2 + (42 + -42x + -24x2) + -1(x2 + -4x + 2) = 0

Reorder the terms:
3 + -5x + 6x2 + 42 + -42x + -24x2 + -1(2 + -4x + x2) = 0
3 + -5x + 6x2 + 42 + -42x + -24x2 + (2 * -1 + -4x * -1 + x2 * -1) = 0
3 + -5x + 6x2 + 42 + -42x + -24x2 + (-2 + 4x + -1x2) = 0

Reorder the terms:
3 + 42 + -2 + -5x + -42x + 4x + 6x2 + -24x2 + -1x2 = 0

Combine like terms: 3 + 42 = 45
45 + -2 + -5x + -42x + 4x + 6x2 + -24x2 + -1x2 = 0

Combine like terms: 45 + -2 = 43
43 + -5x + -42x + 4x + 6x2 + -24x2 + -1x2 = 0

Combine like terms: -5x + -42x = -47x
43 + -47x + 4x + 6x2 + -24x2 + -1x2 = 0

Combine like terms: -47x + 4x = -43x
43 + -43x + 6x2 + -24x2 + -1x2 = 0

Combine like terms: 6x2 + -24x2 = -18x2
43 + -43x + -18x2 + -1x2 = 0

Combine like terms: -18x2 + -1x2 = -19x2
43 + -43x + -19x2 = 0

Solving
43 + -43x + -19x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-19 the coefficient of the squared term: 

Divide each side by '-19'.
-2.263157895 + 2.263157895x + x2 = 0

Move the constant term to the right:

Add '2.263157895' to each side of the equation.
-2.263157895 + 2.263157895x + 2.263157895 + x2 = 0 + 2.263157895

Reorder the terms:
-2.263157895 + 2.263157895 + 2.263157895x + x2 = 0 + 2.263157895

Combine like terms: -2.263157895 + 2.263157895 = 0.000000000
0.000000000 + 2.263157895x + x2 = 0 + 2.263157895
2.263157895x + x2 = 0 + 2.263157895

Combine like terms: 0 + 2.263157895 = 2.263157895
2.263157895x + x2 = 2.263157895

The x term is 2.263157895x.  Take half its coefficient (1.131578948).
Square it (1.280470916) and add it to both sides.

Add '1.280470916' to each side of the equation.
2.263157895x + 1.280470916 + x2 = 2.263157895 + 1.280470916

Reorder the terms:
1.280470916 + 2.263157895x + x2 = 2.263157895 + 1.280470916

Combine like terms: 2.263157895 + 1.280470916 = 3.543628811
1.280470916 + 2.263157895x + x2 = 3.543628811

Factor a perfect square on the left side:
(x + 1.131578948)(x + 1.131578948) = 3.543628811

Calculate the square root of the right side: 1.882452871

Break this problem into two subproblems by setting 
(x + 1.131578948) equal to 1.882452871 and -1.882452871.


Subproblem 1
x + 1.131578948 = 1.882452871

Simplifying
x + 1.131578948 = 1.882452871

Reorder the terms:
1.131578948 + x = 1.882452871

Solving
1.131578948 + x = 1.882452871

Solving for variable 'x'.

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

Add '-1.131578948' to each side of the equation.
1.131578948 + -1.131578948 + x = 1.882452871 + -1.131578948

Combine like terms: 1.131578948 + -1.131578948 = 0.000000000
0.000000000 + x = 1.882452871 + -1.131578948
x = 1.882452871 + -1.131578948

Combine like terms: 1.882452871 + -1.131578948 = 0.750873923
x = 0.750873923

Simplifying
x = 0.750873923


Subproblem 2
x + 1.131578948 = -1.882452871

Simplifying
x + 1.131578948 = -1.882452871

Reorder the terms:
1.131578948 + x = -1.882452871

Solving
1.131578948 + x = -1.882452871

Solving for variable 'x'.

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

Add '-1.131578948' to each side of the equation.
1.131578948 + -1.131578948 + x = -1.882452871 + -1.131578948

Combine like terms: 1.131578948 + -1.131578948 = 0.000000000
0.000000000 + x = -1.882452871 + -1.131578948
x = -1.882452871 + -1.131578948

Combine like terms: -1.882452871 + -1.131578948 = -3.014031819
x = -3.014031819

Simplifying
x = -3.014031819


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.750873923, -3.014031819}

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