5(8-2)-x(3x-7)=-6(4x-6x)+x+4.31662479

Solution for 5(8-2)-x(3x-7)=-6(4x-6x)+x+4.31662479 equation:

Simplifying
5(8 + -2) + -1x(3x + -7) = -6(4x + -6x) + x + 4.31662479

Combine like terms: 8 + -2 = 6
5(6) + -1x(3x + -7) = -6(4x + -6x) + x + 4.31662479

Multiply 5 * 6
30 + -1x(3x + -7) = -6(4x + -6x) + x + 4.31662479

Reorder the terms:
30 + -1x(-7 + 3x) = -6(4x + -6x) + x + 4.31662479
30 + (-7 * -1x + 3x * -1x) = -6(4x + -6x) + x + 4.31662479
30 + (7x + -3x2) = -6(4x + -6x) + x + 4.31662479

Combine like terms: 4x + -6x = -2x
30 + 7x + -3x2 = -6(-2x) + x + 4.31662479

Remove parenthesis around (-2x)
30 + 7x + -3x2 = -6 * -2x + x + 4.31662479

Multiply -6 * -2
30 + 7x + -3x2 = 12x + x + 4.31662479

Reorder the terms:
30 + 7x + -3x2 = 4.31662479 + 12x + x

Combine like terms: 12x + x = 13x
30 + 7x + -3x2 = 4.31662479 + 13x

Solving
30 + 7x + -3x2 = 4.31662479 + 13x

Solving for variable 'x'.

Reorder the terms:
30 + -4.31662479 + 7x + -13x + -3x2 = 4.31662479 + 13x + -4.31662479 + -13x

Combine like terms: 30 + -4.31662479 = 25.68337521
25.68337521 + 7x + -13x + -3x2 = 4.31662479 + 13x + -4.31662479 + -13x

Combine like terms: 7x + -13x = -6x
25.68337521 + -6x + -3x2 = 4.31662479 + 13x + -4.31662479 + -13x

Reorder the terms:
25.68337521 + -6x + -3x2 = 4.31662479 + -4.31662479 + 13x + -13x

Combine like terms: 4.31662479 + -4.31662479 = 0.00000000
25.68337521 + -6x + -3x2 = 0.00000000 + 13x + -13x
25.68337521 + -6x + -3x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
25.68337521 + -6x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-8.56112507 + 2x + x2 = 0

Move the constant term to the right:

Add '8.56112507' to each side of the equation.
-8.56112507 + 2x + 8.56112507 + x2 = 0 + 8.56112507

Reorder the terms:
-8.56112507 + 8.56112507 + 2x + x2 = 0 + 8.56112507

Combine like terms: -8.56112507 + 8.56112507 = 0.00000000
0.00000000 + 2x + x2 = 0 + 8.56112507
2x + x2 = 0 + 8.56112507

Combine like terms: 0 + 8.56112507 = 8.56112507
2x + x2 = 8.56112507

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 8.56112507 + 1

Reorder the terms:
1 + 2x + x2 = 8.56112507 + 1

Combine like terms: 8.56112507 + 1 = 9.56112507
1 + 2x + x2 = 9.56112507

Factor a perfect square on the left side:
(x + 1)(x + 1) = 9.56112507

Calculate the square root of the right side: 3.092106898

Break this problem into two subproblems by setting 
(x + 1) equal to 3.092106898 and -3.092106898.

Subproblem 1
x + 1 = 3.092106898

Simplifying
x + 1 = 3.092106898

Reorder the terms:
1 + x = 3.092106898

Solving
1 + x = 3.092106898

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.092106898 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.092106898 + -1
x = 3.092106898 + -1

Combine like terms: 3.092106898 + -1 = 2.092106898
x = 2.092106898

Simplifying
x = 2.092106898

Subproblem 2
x + 1 = -3.092106898

Simplifying
x + 1 = -3.092106898

Reorder the terms:
1 + x = -3.092106898

Solving
1 + x = -3.092106898

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.092106898 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.092106898 + -1
x = -3.092106898 + -1

Combine like terms: -3.092106898 + -1 = -4.092106898
x = -4.092106898

Simplifying
x = -4.092106898

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.092106898, -4.092106898}