-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 = 5x
-7 + -7x = (-9 + 5x + 4x2)

Solving
-7 + -7x = -9 + 5x + 4x2

Solving for variable 'x'.

Reorder the terms:
-7 + 9 + -7x + -5x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2

Combine like terms: -7 + 9 = 2
2 + -7x + -5x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2

Combine like terms: -7x + -5x = -12x
2 + -12x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2

Reorder the terms:
2 + -12x + -4x2 = -9 + 9 + 5x + -5x + 4x2 + -4x2

Combine like terms: -9 + 9 = 0
2 + -12x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
2 + -12x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
2 + -12x + -4x2 = 0 + 4x2 + -4x2
2 + -12x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
2 + -12x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -6x + -2x2)' equal to zero and attempt to solve:

Simplifying
1 + -6x + -2x2 = 0

Solving
1 + -6x + -2x2 = 0

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

Divide each side by '-2'.
-0.5 + 3x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 3x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3x + x2 = 0 + 0.5
3x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3x + x2 = 0.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 0.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + 3x + x2 = 2.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.658312395 and -1.658312395.

Subproblem 1
x + 1.5 = 1.658312395

Simplifying
x + 1.5 = 1.658312395

Reorder the terms:
1.5 + x = 1.658312395

Solving
1.5 + x = 1.658312395

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.658312395 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.658312395 + -1.5
x = 1.658312395 + -1.5

Combine like terms: 1.658312395 + -1.5 = 0.158312395
x = 0.158312395

Simplifying
x = 0.158312395

Subproblem 2
x + 1.5 = -1.658312395

Simplifying
x + 1.5 = -1.658312395

Reorder the terms:
1.5 + x = -1.658312395

Solving
1.5 + x = -1.658312395

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.658312395 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.658312395 + -1.5
x = -1.658312395 + -1.5

Combine like terms: -1.658312395 + -1.5 = -3.158312395
x = -3.158312395

Simplifying
x = -3.158312395

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.158312395, -3.158312395}
Solution
x = {0.158312395, -3.158312395}