35-35x=(6x+1)(x+1)

Solution for 35-35x=(6x+1)(x+1) equation:

Simplifying
35 + -35x = (6x + 1)(x + 1)

Reorder the terms:
35 + -35x = (1 + 6x)(x + 1)

Reorder the terms:
35 + -35x = (1 + 6x)(1 + x)

Multiply (1 + 6x) * (1 + x)
35 + -35x = (1(1 + x) + 6x * (1 + x))
35 + -35x = ((1 * 1 + x * 1) + 6x * (1 + x))
35 + -35x = ((1 + 1x) + 6x * (1 + x))
35 + -35x = (1 + 1x + (1 * 6x + x * 6x))
35 + -35x = (1 + 1x + (6x + 6x2))

Combine like terms: 1x + 6x = 7x
35 + -35x = (1 + 7x + 6x2)

Solving
35 + -35x = 1 + 7x + 6x2

Solving for variable 'x'.

Reorder the terms:
35 + -1 + -35x + -7x + -6x2 = 1 + 7x + 6x2 + -1 + -7x + -6x2

Combine like terms: 35 + -1 = 34
34 + -35x + -7x + -6x2 = 1 + 7x + 6x2 + -1 + -7x + -6x2

Combine like terms: -35x + -7x = -42x
34 + -42x + -6x2 = 1 + 7x + 6x2 + -1 + -7x + -6x2

Reorder the terms:
34 + -42x + -6x2 = 1 + -1 + 7x + -7x + 6x2 + -6x2

Combine like terms: 1 + -1 = 0
34 + -42x + -6x2 = 0 + 7x + -7x + 6x2 + -6x2
34 + -42x + -6x2 = 7x + -7x + 6x2 + -6x2

Combine like terms: 7x + -7x = 0
34 + -42x + -6x2 = 0 + 6x2 + -6x2
34 + -42x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
34 + -42x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -21x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(17 + -21x + -3x2)' equal to zero and attempt to solve:

Simplifying
17 + -21x + -3x2 = 0

Solving
17 + -21x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-5.666666667 + 7x + x2 = 0

Move the constant term to the right:

Add '5.666666667' to each side of the equation.
-5.666666667 + 7x + 5.666666667 + x2 = 0 + 5.666666667

Reorder the terms:
-5.666666667 + 5.666666667 + 7x + x2 = 0 + 5.666666667

Combine like terms: -5.666666667 + 5.666666667 = 0.000000000
0.000000000 + 7x + x2 = 0 + 5.666666667
7x + x2 = 0 + 5.666666667

Combine like terms: 0 + 5.666666667 = 5.666666667
7x + x2 = 5.666666667

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 5.666666667 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 5.666666667 + 12.25

Combine like terms: 5.666666667 + 12.25 = 17.916666667
12.25 + 7x + x2 = 17.916666667

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 17.916666667

Calculate the square root of the right side: 4.232808366

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.232808366 and -4.232808366.

Subproblem 1
x + 3.5 = 4.232808366

Simplifying
x + 3.5 = 4.232808366

Reorder the terms:
3.5 + x = 4.232808366

Solving
3.5 + x = 4.232808366

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.232808366 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.232808366 + -3.5
x = 4.232808366 + -3.5

Combine like terms: 4.232808366 + -3.5 = 0.732808366
x = 0.732808366

Simplifying
x = 0.732808366

Subproblem 2
x + 3.5 = -4.232808366

Simplifying
x + 3.5 = -4.232808366

Reorder the terms:
3.5 + x = -4.232808366

Solving
3.5 + x = -4.232808366

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.232808366 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.232808366 + -3.5
x = -4.232808366 + -3.5

Combine like terms: -4.232808366 + -3.5 = -7.732808366
x = -7.732808366

Simplifying
x = -7.732808366

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.732808366, -7.732808366}
Solution
x = {0.732808366, -7.732808366}