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

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

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

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

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

Reorder the terms:
x + -1[5 + 3x + -1(-6 + 2x)] = 4 + -1[7x(6 + 3x)]
x + -1[5 + 3x + (-6 * -1 + 2x * -1)] = 4 + -1[7x(6 + 3x)]
x + -1[5 + 3x + (6 + -2x)] = 4 + -1[7x(6 + 3x)]

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

Combine like terms: 5 + 6 = 11
x + -1[11 + 3x + -2x] = 4 + -1[7x(6 + 3x)]

Combine like terms: 3x + -2x = 1x
x + -1[11 + 1x] = 4 + -1[7x(6 + 3x)]
x + [11 * -1 + 1x * -1] = 4 + -1[7x(6 + 3x)]
x + [-11 + -1x] = 4 + -1[7x(6 + 3x)]

Reorder the terms:
-11 + x + -1x = 4 + -1[7x(6 + 3x)]

Combine like terms: x + -1x = 0
-11 + 0 = 4 + -1[7x(6 + 3x)]
-11 = 4 + -1[7x(6 + 3x)]
-11 = 4 + -1[(6 * 7x + 3x * 7x)]
-11 = 4 + -1[(42x + 21x2)]
-11 = 4 + [42x * -1 + 21x2 * -1]
-11 = 4 + [-42x + -21x2]

Solving
-11 = 4 + -42x + -21x2

Solving for variable 'x'.

Combine like terms: -11 + -4 = -15
-15 + 42x + 21x2 = 4 + -42x + -21x2 + -4 + 42x + 21x2

Reorder the terms:
-15 + 42x + 21x2 = 4 + -4 + -42x + 42x + -21x2 + 21x2

Combine like terms: 4 + -4 = 0
-15 + 42x + 21x2 = 0 + -42x + 42x + -21x2 + 21x2
-15 + 42x + 21x2 = -42x + 42x + -21x2 + 21x2

Combine like terms: -42x + 42x = 0
-15 + 42x + 21x2 = 0 + -21x2 + 21x2
-15 + 42x + 21x2 = -21x2 + 21x2

Combine like terms: -21x2 + 21x2 = 0
-15 + 42x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 14x + 7x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + 14x + 7x2)' equal to zero and attempt to solve:

Simplifying
-5 + 14x + 7x2 = 0

Solving
-5 + 14x + 7x2 = 0

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

Divide each side by '7'.
-0.7142857143 + 2x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 2x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 2x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + 0.7142857143
2x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
2x + x2 = 0.7142857143

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 = 0.7142857143 + 1

Reorder the terms:
1 + 2x + x2 = 0.7142857143 + 1

Combine like terms: 0.7142857143 + 1 = 1.7142857143
1 + 2x + x2 = 1.7142857143

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.7142857143

Calculate the square root of the right side: 1.309307341

Break this problem into two subproblems by setting 
(x + 1) equal to 1.309307341 and -1.309307341.

Subproblem 1
x + 1 = 1.309307341

Simplifying
x + 1 = 1.309307341

Reorder the terms:
1 + x = 1.309307341

Solving
1 + x = 1.309307341

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 = 1.309307341 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.309307341 + -1
x = 1.309307341 + -1

Combine like terms: 1.309307341 + -1 = 0.309307341
x = 0.309307341

Simplifying
x = 0.309307341

Subproblem 2
x + 1 = -1.309307341

Simplifying
x + 1 = -1.309307341

Reorder the terms:
1 + x = -1.309307341

Solving
1 + x = -1.309307341

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 = -1.309307341 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.309307341 + -1
x = -1.309307341 + -1

Combine like terms: -1.309307341 + -1 = -2.309307341
x = -2.309307341

Simplifying
x = -2.309307341

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.309307341, -2.309307341}
Solution
x = {0.309307341, -2.309307341}