7-7x=(4x+9)(x+1)

Solution for 7-7x=(4x+9)(x+1) equation:

Simplifying
7 + -7x = (4x + 9)(x + 1)

Reorder the terms:
7 + -7x = (9 + 4x)(x + 1)

Reorder the terms:
7 + -7x = (9 + 4x)(1 + x)

Multiply (9 + 4x) * (1 + x)
7 + -7x = (9(1 + x) + 4x * (1 + x))
7 + -7x = ((1 * 9 + x * 9) + 4x * (1 + x))
7 + -7x = ((9 + 9x) + 4x * (1 + x))
7 + -7x = (9 + 9x + (1 * 4x + x * 4x))
7 + -7x = (9 + 9x + (4x + 4x2))

Combine like terms: 9x + 4x = 13x
7 + -7x = (9 + 13x + 4x2)

Solving
7 + -7x = 9 + 13x + 4x2

Solving for variable 'x'.

Reorder the terms:
7 + -9 + -7x + -13x + -4x2 = 9 + 13x + 4x2 + -9 + -13x + -4x2

Combine like terms: 7 + -9 = -2
-2 + -7x + -13x + -4x2 = 9 + 13x + 4x2 + -9 + -13x + -4x2

Combine like terms: -7x + -13x = -20x
-2 + -20x + -4x2 = 9 + 13x + 4x2 + -9 + -13x + -4x2

Reorder the terms:
-2 + -20x + -4x2 = 9 + -9 + 13x + -13x + 4x2 + -4x2

Combine like terms: 9 + -9 = 0
-2 + -20x + -4x2 = 0 + 13x + -13x + 4x2 + -4x2
-2 + -20x + -4x2 = 13x + -13x + 4x2 + -4x2

Combine like terms: 13x + -13x = 0
-2 + -20x + -4x2 = 0 + 4x2 + -4x2
-2 + -20x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-2 + -20x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 10x + 2x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(1 + 10x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + 10x + 2x2 = 0

Solving
1 + 10x + 2x2 = 0

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

Divide each side by '2'.
0.5 + 5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 5x + x2 = 0 + -0.5
5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
5x + x2 = -0.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -0.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -0.5 + 6.25

Combine like terms: -0.5 + 6.25 = 5.75
6.25 + 5x + x2 = 5.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.397915762 and -2.397915762.

Subproblem 1
x + 2.5 = 2.397915762

Simplifying
x + 2.5 = 2.397915762

Reorder the terms:
2.5 + x = 2.397915762

Solving
2.5 + x = 2.397915762

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.397915762 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.397915762 + -2.5
x = 2.397915762 + -2.5

Combine like terms: 2.397915762 + -2.5 = -0.102084238
x = -0.102084238

Simplifying
x = -0.102084238

Subproblem 2
x + 2.5 = -2.397915762

Simplifying
x + 2.5 = -2.397915762

Reorder the terms:
2.5 + x = -2.397915762

Solving
2.5 + x = -2.397915762

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.397915762 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.397915762 + -2.5
x = -2.397915762 + -2.5

Combine like terms: -2.397915762 + -2.5 = -4.897915762
x = -4.897915762

Simplifying
x = -4.897915762

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.102084238, -4.897915762}
Solution
x = {-0.102084238, -4.897915762}