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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: 7x + -13x = -6x
30 + -6x + -3x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
30 + -6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -2x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(10 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
10 + -2x + -1x2 = 0

Solving
10 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10 + 2x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 2x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 2x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 2x + x2 = 0 + 10
2x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
2x + x2 = 10

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 = 10 + 1

Reorder the terms:
1 + 2x + x2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + 2x + x2 = 11

Factor a perfect square on the left side:
(x + 1)(x + 1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 1) equal to 3.31662479 and -3.31662479.

Subproblem 1
x + 1 = 3.31662479

Simplifying
x + 1 = 3.31662479

Reorder the terms:
1 + x = 3.31662479

Solving
1 + x = 3.31662479

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 = 3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.31662479 + -1
x = 3.31662479 + -1

Combine like terms: 3.31662479 + -1 = 2.31662479
x = 2.31662479

Simplifying
x = 2.31662479

Subproblem 2
x + 1 = -3.31662479

Simplifying
x + 1 = -3.31662479

Reorder the terms:
1 + x = -3.31662479

Solving
1 + x = -3.31662479

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 = -3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.31662479 + -1
x = -3.31662479 + -1

Combine like terms: -3.31662479 + -1 = -4.31662479
x = -4.31662479

Simplifying
x = -4.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.31662479, -4.31662479}
Solution
x = {2.31662479, -4.31662479}