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

Solution for 9x-4=(x-5)(9x+4) equation:

Simplifying
9x + -4 = (x + -5)(9x + 4)

Reorder the terms:
-4 + 9x = (x + -5)(9x + 4)

Reorder the terms:
-4 + 9x = (-5 + x)(9x + 4)

Reorder the terms:
-4 + 9x = (-5 + x)(4 + 9x)

Multiply (-5 + x) * (4 + 9x)
-4 + 9x = (-5(4 + 9x) + x(4 + 9x))
-4 + 9x = ((4 * -5 + 9x * -5) + x(4 + 9x))
-4 + 9x = ((-20 + -45x) + x(4 + 9x))
-4 + 9x = (-20 + -45x + (4 * x + 9x * x))
-4 + 9x = (-20 + -45x + (4x + 9x2))

Combine like terms: -45x + 4x = -41x
-4 + 9x = (-20 + -41x + 9x2)

Solving
-4 + 9x = -20 + -41x + 9x2

Solving for variable 'x'.

Reorder the terms:
-4 + 20 + 9x + 41x + -9x2 = -20 + -41x + 9x2 + 20 + 41x + -9x2

Combine like terms: -4 + 20 = 16
16 + 9x + 41x + -9x2 = -20 + -41x + 9x2 + 20 + 41x + -9x2

Combine like terms: 9x + 41x = 50x
16 + 50x + -9x2 = -20 + -41x + 9x2 + 20 + 41x + -9x2

Reorder the terms:
16 + 50x + -9x2 = -20 + 20 + -41x + 41x + 9x2 + -9x2

Combine like terms: -20 + 20 = 0
16 + 50x + -9x2 = 0 + -41x + 41x + 9x2 + -9x2
16 + 50x + -9x2 = -41x + 41x + 9x2 + -9x2

Combine like terms: -41x + 41x = 0
16 + 50x + -9x2 = 0 + 9x2 + -9x2
16 + 50x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
16 + 50x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-1.777777778 + -5.555555556x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + -5.555555556x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + -5.555555556x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + -5.555555556x + x2 = 0 + 1.777777778
-5.555555556x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
-5.555555556x + x2 = 1.777777778

The x term is -5.555555556x.  Take half its coefficient (-2.777777778).
Square it (7.716049384) and add it to both sides.

Add '7.716049384' to each side of the equation.
-5.555555556x + 7.716049384 + x2 = 1.777777778 + 7.716049384

Reorder the terms:
7.716049384 + -5.555555556x + x2 = 1.777777778 + 7.716049384

Combine like terms: 1.777777778 + 7.716049384 = 9.493827162
7.716049384 + -5.555555556x + x2 = 9.493827162

Factor a perfect square on the left side:
(x + -2.777777778)(x + -2.777777778) = 9.493827162

Calculate the square root of the right side: 3.081205472

Break this problem into two subproblems by setting 
(x + -2.777777778) equal to 3.081205472 and -3.081205472.

Subproblem 1
x + -2.777777778 = 3.081205472

Simplifying
x + -2.777777778 = 3.081205472

Reorder the terms:
-2.777777778 + x = 3.081205472

Solving
-2.777777778 + x = 3.081205472

Solving for variable 'x'.

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

Add '2.777777778' to each side of the equation.
-2.777777778 + 2.777777778 + x = 3.081205472 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + x = 3.081205472 + 2.777777778
x = 3.081205472 + 2.777777778

Combine like terms: 3.081205472 + 2.777777778 = 5.85898325
x = 5.85898325

Simplifying
x = 5.85898325

Subproblem 2
x + -2.777777778 = -3.081205472

Simplifying
x + -2.777777778 = -3.081205472

Reorder the terms:
-2.777777778 + x = -3.081205472

Solving
-2.777777778 + x = -3.081205472

Solving for variable 'x'.

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

Add '2.777777778' to each side of the equation.
-2.777777778 + 2.777777778 + x = -3.081205472 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + x = -3.081205472 + 2.777777778
x = -3.081205472 + 2.777777778

Combine like terms: -3.081205472 + 2.777777778 = -0.303427694
x = -0.303427694

Simplifying
x = -0.303427694

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.85898325, -0.303427694}