100+(-8x-(20+4x))=60-6x(6x+(50-4x))+10

Solution for 100+(-8x-(20+4x))=60-6x(6x+(50-4x))+10 equation:

Simplifying
100 + (-8x + -1(20 + 4x)) = 60 + -6x(6x + (50 + -4x)) + 10
100 + (-8x + (20 * -1 + 4x * -1)) = 60 + -6x(6x + (50 + -4x)) + 10
100 + (-8x + (-20 + -4x)) = 60 + -6x(6x + (50 + -4x)) + 10

Reorder the terms:
100 + (-20 + -8x + -4x) = 60 + -6x(6x + (50 + -4x)) + 10

Combine like terms: -8x + -4x = -12x
100 + (-20 + -12x) = 60 + -6x(6x + (50 + -4x)) + 10

Remove parenthesis around (-20 + -12x)
100 + -20 + -12x = 60 + -6x(6x + (50 + -4x)) + 10

Combine like terms: 100 + -20 = 80
80 + -12x = 60 + -6x(6x + (50 + -4x)) + 10

Remove parenthesis around (50 + -4x)
80 + -12x = 60 + -6x(6x + 50 + -4x) + 10

Reorder the terms:
80 + -12x = 60 + -6x(50 + 6x + -4x) + 10

Combine like terms: 6x + -4x = 2x
80 + -12x = 60 + -6x(50 + 2x) + 10
80 + -12x = 60 + (50 * -6x + 2x * -6x) + 10
80 + -12x = 60 + (-300x + -12x2) + 10

Reorder the terms:
80 + -12x = 60 + 10 + -300x + -12x2

Combine like terms: 60 + 10 = 70
80 + -12x = 70 + -300x + -12x2

Solving
80 + -12x = 70 + -300x + -12x2

Solving for variable 'x'.

Reorder the terms:
80 + -70 + -12x + 300x + 12x2 = 70 + -300x + -12x2 + -70 + 300x + 12x2

Combine like terms: 80 + -70 = 10
10 + -12x + 300x + 12x2 = 70 + -300x + -12x2 + -70 + 300x + 12x2

Combine like terms: -12x + 300x = 288x
10 + 288x + 12x2 = 70 + -300x + -12x2 + -70 + 300x + 12x2

Reorder the terms:
10 + 288x + 12x2 = 70 + -70 + -300x + 300x + -12x2 + 12x2

Combine like terms: 70 + -70 = 0
10 + 288x + 12x2 = 0 + -300x + 300x + -12x2 + 12x2
10 + 288x + 12x2 = -300x + 300x + -12x2 + 12x2

Combine like terms: -300x + 300x = 0
10 + 288x + 12x2 = 0 + -12x2 + 12x2
10 + 288x + 12x2 = -12x2 + 12x2

Combine like terms: -12x2 + 12x2 = 0
10 + 288x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 144x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 144x + 6x2)' equal to zero and attempt to solve:

Simplifying
5 + 144x + 6x2 = 0

Solving
5 + 144x + 6x2 = 0

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

Divide each side by '6'.
0.8333333333 + 24x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + 24x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + 24x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + 24x + x2 = 0 + -0.8333333333
24x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
24x + x2 = -0.8333333333

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = -0.8333333333 + 144

Reorder the terms:
144 + 24x + x2 = -0.8333333333 + 144

Combine like terms: -0.8333333333 + 144 = 143.1666666667
144 + 24x + x2 = 143.1666666667

Factor a perfect square on the left side:
(x + 12)(x + 12) = 143.1666666667

Calculate the square root of the right side: 11.965227397

Break this problem into two subproblems by setting 
(x + 12) equal to 11.965227397 and -11.965227397.

Subproblem 1
x + 12 = 11.965227397

Simplifying
x + 12 = 11.965227397

Reorder the terms:
12 + x = 11.965227397

Solving
12 + x = 11.965227397

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = 11.965227397 + -12

Combine like terms: 12 + -12 = 0
0 + x = 11.965227397 + -12
x = 11.965227397 + -12

Combine like terms: 11.965227397 + -12 = -0.034772603
x = -0.034772603

Simplifying
x = -0.034772603

Subproblem 2
x + 12 = -11.965227397

Simplifying
x + 12 = -11.965227397

Reorder the terms:
12 + x = -11.965227397

Solving
12 + x = -11.965227397

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = -11.965227397 + -12

Combine like terms: 12 + -12 = 0
0 + x = -11.965227397 + -12
x = -11.965227397 + -12

Combine like terms: -11.965227397 + -12 = -23.965227397
x = -23.965227397

Simplifying
x = -23.965227397

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.034772603, -23.965227397}
Solution
x = {-0.034772603, -23.965227397}