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

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

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

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

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

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

Combine like terms: 9x + -4x = 5x
7 + -1x = (-9 + 5x + 4x2)

Solving
7 + -1x = -9 + 5x + 4x2

Solving for variable 'x'.

Reorder the terms:
7 + 9 + -1x + -5x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2

Combine like terms: 7 + 9 = 16
16 + -1x + -5x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2

Combine like terms: -1x + -5x = -6x
16 + -6x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2

Reorder the terms:
16 + -6x + -4x2 = -9 + 9 + 5x + -5x + 4x2 + -4x2

Combine like terms: -9 + 9 = 0
16 + -6x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
16 + -6x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
16 + -6x + -4x2 = 0 + 4x2 + -4x2
16 + -6x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
16 + -6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -3x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -3x + -2x2)' equal to zero and attempt to solve:

Simplifying
8 + -3x + -2x2 = 0

Solving
8 + -3x + -2x2 = 0

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

Divide each side by '-2'.
-4 + 1.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 1.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1.5x + x2 = 0 + 4
1.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
1.5x + x2 = 4

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 4 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 4 + 0.5625

Combine like terms: 4 + 0.5625 = 4.5625
0.5625 + 1.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.136000936 and -2.136000936.

Subproblem 1
x + 0.75 = 2.136000936

Simplifying
x + 0.75 = 2.136000936

Reorder the terms:
0.75 + x = 2.136000936

Solving
0.75 + x = 2.136000936

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 2.136000936 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 2.136000936 + -0.75
x = 2.136000936 + -0.75

Combine like terms: 2.136000936 + -0.75 = 1.386000936
x = 1.386000936

Simplifying
x = 1.386000936

Subproblem 2
x + 0.75 = -2.136000936

Simplifying
x + 0.75 = -2.136000936

Reorder the terms:
0.75 + x = -2.136000936

Solving
0.75 + x = -2.136000936

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -2.136000936 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -2.136000936 + -0.75
x = -2.136000936 + -0.75

Combine like terms: -2.136000936 + -0.75 = -2.886000936
x = -2.886000936

Simplifying
x = -2.886000936

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.386000936, -2.886000936}
Solution
x = {1.386000936, -2.886000936}