-(1+7x)6(-7-x)=36

Solution for -(1+7x)6(-7-x)=36 equation:

Simplifying
-1(1 + 7x) * 6(-7 + -1x) = 36

Reorder the terms for easier multiplication:
-1 * 6(1 + 7x)(-7 + -1x) = 36

Multiply -1 * 6
-6(1 + 7x)(-7 + -1x) = 36

Multiply (1 + 7x) * (-7 + -1x)
-6(1(-7 + -1x) + 7x * (-7 + -1x)) = 36
-6((-7 * 1 + -1x * 1) + 7x * (-7 + -1x)) = 36
-6((-7 + -1x) + 7x * (-7 + -1x)) = 36
-6(-7 + -1x + (-7 * 7x + -1x * 7x)) = 36
-6(-7 + -1x + (-49x + -7x2)) = 36

Combine like terms: -1x + -49x = -50x
-6(-7 + -50x + -7x2) = 36
(-7 * -6 + -50x * -6 + -7x2 * -6) = 36
(42 + 300x + 42x2) = 36

Solving
42 + 300x + 42x2 = 36

Solving for variable 'x'.

Reorder the terms:
42 + -36 + 300x + 42x2 = 36 + -36

Combine like terms: 42 + -36 = 6
6 + 300x + 42x2 = 36 + -36

Combine like terms: 36 + -36 = 0
6 + 300x + 42x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 50x + 7x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + 50x + 7x2)' equal to zero and attempt to solve:

Simplifying
1 + 50x + 7x2 = 0

Solving
1 + 50x + 7x2 = 0

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

Divide each side by '7'.
0.1428571429 + 7.142857143x + x2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + 7.142857143x + -0.1428571429 + x2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + 7.142857143x + x2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + 7.142857143x + x2 = 0 + -0.1428571429
7.142857143x + x2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
7.142857143x + x2 = -0.1428571429

The x term is 7.142857143x.  Take half its coefficient (3.571428572).
Square it (12.75510204) and add it to both sides.

Add '12.75510204' to each side of the equation.
7.142857143x + 12.75510204 + x2 = -0.1428571429 + 12.75510204

Reorder the terms:
12.75510204 + 7.142857143x + x2 = -0.1428571429 + 12.75510204

Combine like terms: -0.1428571429 + 12.75510204 = 12.6122448971
12.75510204 + 7.142857143x + x2 = 12.6122448971

Factor a perfect square on the left side:
(x + 3.571428572)(x + 3.571428572) = 12.6122448971

Calculate the square root of the right side: 3.551372255

Break this problem into two subproblems by setting 
(x + 3.571428572) equal to 3.551372255 and -3.551372255.

Subproblem 1
x + 3.571428572 = 3.551372255

Simplifying
x + 3.571428572 = 3.551372255

Reorder the terms:
3.571428572 + x = 3.551372255

Solving
3.571428572 + x = 3.551372255

Solving for variable 'x'.

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

Add '-3.571428572' to each side of the equation.
3.571428572 + -3.571428572 + x = 3.551372255 + -3.571428572

Combine like terms: 3.571428572 + -3.571428572 = 0.000000000
0.000000000 + x = 3.551372255 + -3.571428572
x = 3.551372255 + -3.571428572

Combine like terms: 3.551372255 + -3.571428572 = -0.020056317
x = -0.020056317

Simplifying
x = -0.020056317

Subproblem 2
x + 3.571428572 = -3.551372255

Simplifying
x + 3.571428572 = -3.551372255

Reorder the terms:
3.571428572 + x = -3.551372255

Solving
3.571428572 + x = -3.551372255

Solving for variable 'x'.

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

Add '-3.571428572' to each side of the equation.
3.571428572 + -3.571428572 + x = -3.551372255 + -3.571428572

Combine like terms: 3.571428572 + -3.571428572 = 0.000000000
0.000000000 + x = -3.551372255 + -3.571428572
x = -3.551372255 + -3.571428572

Combine like terms: -3.551372255 + -3.571428572 = -7.122800827
x = -7.122800827

Simplifying
x = -7.122800827

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.020056317, -7.122800827}
Solution
x = {-0.020056317, -7.122800827}