-(1+7x)16(-7-x)=36

Solution for -(1+7x)16(-7-x)=36 equation:

Simplifying
-1(1 + 7x) * 16(-7 + -1x) = 36

Reorder the terms for easier multiplication:
-1 * 16(1 + 7x)(-7 + -1x) = 36

Multiply -1 * 16
-16(1 + 7x)(-7 + -1x) = 36

Multiply (1 + 7x) * (-7 + -1x)
-16(1(-7 + -1x) + 7x * (-7 + -1x)) = 36
-16((-7 * 1 + -1x * 1) + 7x * (-7 + -1x)) = 36
-16((-7 + -1x) + 7x * (-7 + -1x)) = 36
-16(-7 + -1x + (-7 * 7x + -1x * 7x)) = 36
-16(-7 + -1x + (-49x + -7x2)) = 36

Combine like terms: -1x + -49x = -50x
-16(-7 + -50x + -7x2) = 36
(-7 * -16 + -50x * -16 + -7x2 * -16) = 36
(112 + 800x + 112x2) = 36

Solving
112 + 800x + 112x2 = 36

Solving for variable 'x'.

Reorder the terms:
112 + -36 + 800x + 112x2 = 36 + -36

Combine like terms: 112 + -36 = 76
76 + 800x + 112x2 = 36 + -36

Combine like terms: 36 + -36 = 0
76 + 800x + 112x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(19 + 200x + 28x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(19 + 200x + 28x2)' equal to zero and attempt to solve:

Simplifying
19 + 200x + 28x2 = 0

Solving
19 + 200x + 28x2 = 0

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

Divide each side by '28'.
0.6785714286 + 7.142857143x + x2 = 0

Move the constant term to the right:

Add '-0.6785714286' to each side of the equation.
0.6785714286 + 7.142857143x + -0.6785714286 + x2 = 0 + -0.6785714286

Reorder the terms:
0.6785714286 + -0.6785714286 + 7.142857143x + x2 = 0 + -0.6785714286

Combine like terms: 0.6785714286 + -0.6785714286 = 0.0000000000
0.0000000000 + 7.142857143x + x2 = 0 + -0.6785714286
7.142857143x + x2 = 0 + -0.6785714286

Combine like terms: 0 + -0.6785714286 = -0.6785714286
7.142857143x + x2 = -0.6785714286

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 = -0.6785714286 + 12.75510204

Reorder the terms:
12.75510204 + 7.142857143x + x2 = -0.6785714286 + 12.75510204

Combine like terms: -0.6785714286 + 12.75510204 = 12.0765306114
12.75510204 + 7.142857143x + x2 = 12.0765306114

Factor a perfect square on the left side:
(x + 3.571428572)(x + 3.571428572) = 12.0765306114

Calculate the square root of the right side: 3.475130301

Break this problem into two subproblems by setting 
(x + 3.571428572) equal to 3.475130301 and -3.475130301.

Subproblem 1
x + 3.571428572 = 3.475130301

Simplifying
x + 3.571428572 = 3.475130301

Reorder the terms:
3.571428572 + x = 3.475130301

Solving
3.571428572 + x = 3.475130301

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 = 3.475130301 + -3.571428572

Combine like terms: 3.571428572 + -3.571428572 = 0.000000000
0.000000000 + x = 3.475130301 + -3.571428572
x = 3.475130301 + -3.571428572

Combine like terms: 3.475130301 + -3.571428572 = -0.096298271
x = -0.096298271

Simplifying
x = -0.096298271

Subproblem 2
x + 3.571428572 = -3.475130301

Simplifying
x + 3.571428572 = -3.475130301

Reorder the terms:
3.571428572 + x = -3.475130301

Solving
3.571428572 + x = -3.475130301

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 = -3.475130301 + -3.571428572

Combine like terms: 3.571428572 + -3.571428572 = 0.000000000
0.000000000 + x = -3.475130301 + -3.571428572
x = -3.475130301 + -3.571428572

Combine like terms: -3.475130301 + -3.571428572 = -7.046558873
x = -7.046558873

Simplifying
x = -7.046558873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.096298271, -7.046558873}
Solution
x = {-0.096298271, -7.046558873}