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

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

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

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

Remove parenthesis around (-7x)
-5x * -7x = 6 + 3(8 + 2x)

Reorder the terms for easier multiplication:
-5 * -7x * x = 6 + 3(8 + 2x)

Multiply -5 * -7
35x * x = 6 + 3(8 + 2x)

Multiply x * x
35x2 = 6 + 3(8 + 2x)
35x2 = 6 + (8 * 3 + 2x * 3)
35x2 = 6 + (24 + 6x)

Combine like terms: 6 + 24 = 30
35x2 = 30 + 6x

Solving
35x2 = 30 + 6x

Solving for variable 'x'.

Reorder the terms:
-30 + -6x + 35x2 = 30 + 6x + -30 + -6x

Reorder the terms:
-30 + -6x + 35x2 = 30 + -30 + 6x + -6x

Combine like terms: 30 + -30 = 0
-30 + -6x + 35x2 = 0 + 6x + -6x
-30 + -6x + 35x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-30 + -6x + 35x2 = 0

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

Divide each side by '35'.
-0.8571428571 + -0.1714285714x + x2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -0.1714285714x + 0.8571428571 + x2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -0.1714285714x + x2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -0.1714285714x + x2 = 0 + 0.8571428571
-0.1714285714x + x2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-0.1714285714x + x2 = 0.8571428571

The x term is -0.1714285714x.  Take half its coefficient (-0.0857142857).
Square it (0.007346938773) and add it to both sides.

Add '0.007346938773' to each side of the equation.
-0.1714285714x + 0.007346938773 + x2 = 0.8571428571 + 0.007346938773

Reorder the terms:
0.007346938773 + -0.1714285714x + x2 = 0.8571428571 + 0.007346938773

Combine like terms: 0.8571428571 + 0.007346938773 = 0.864489795873
0.007346938773 + -0.1714285714x + x2 = 0.864489795873

Factor a perfect square on the left side:
(x + -0.0857142857)(x + -0.0857142857) = 0.864489795873

Calculate the square root of the right side: 0.929779434

Break this problem into two subproblems by setting 
(x + -0.0857142857) equal to 0.929779434 and -0.929779434.

Subproblem 1
x + -0.0857142857 = 0.929779434

Simplifying
x + -0.0857142857 = 0.929779434

Reorder the terms:
-0.0857142857 + x = 0.929779434

Solving
-0.0857142857 + x = 0.929779434

Solving for variable 'x'.

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

Add '0.0857142857' to each side of the equation.
-0.0857142857 + 0.0857142857 + x = 0.929779434 + 0.0857142857

Combine like terms: -0.0857142857 + 0.0857142857 = 0.0000000000
0.0000000000 + x = 0.929779434 + 0.0857142857
x = 0.929779434 + 0.0857142857

Combine like terms: 0.929779434 + 0.0857142857 = 1.0154937197
x = 1.0154937197

Simplifying
x = 1.0154937197

Subproblem 2
x + -0.0857142857 = -0.929779434

Simplifying
x + -0.0857142857 = -0.929779434

Reorder the terms:
-0.0857142857 + x = -0.929779434

Solving
-0.0857142857 + x = -0.929779434

Solving for variable 'x'.

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

Add '0.0857142857' to each side of the equation.
-0.0857142857 + 0.0857142857 + x = -0.929779434 + 0.0857142857

Combine like terms: -0.0857142857 + 0.0857142857 = 0.0000000000
0.0000000000 + x = -0.929779434 + 0.0857142857
x = -0.929779434 + 0.0857142857

Combine like terms: -0.929779434 + 0.0857142857 = -0.8440651483
x = -0.8440651483

Simplifying
x = -0.8440651483

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0154937197, -0.8440651483}