(9X-2)-(X+3)=(X-5)(X-7)

Solution for (9X-2)-(X+3)=(X-5)(X-7) equation:

Simplifying
(9X + -2) + -1(X + 3) = (X + -5)(X + -7)

Reorder the terms:
(-2 + 9X) + -1(X + 3) = (X + -5)(X + -7)

Remove parenthesis around (-2 + 9X)
-2 + 9X + -1(X + 3) = (X + -5)(X + -7)

Reorder the terms:
-2 + 9X + -1(3 + X) = (X + -5)(X + -7)
-2 + 9X + (3 * -1 + X * -1) = (X + -5)(X + -7)
-2 + 9X + (-3 + -1X) = (X + -5)(X + -7)

Reorder the terms:
-2 + -3 + 9X + -1X = (X + -5)(X + -7)

Combine like terms: -2 + -3 = -5
-5 + 9X + -1X = (X + -5)(X + -7)

Combine like terms: 9X + -1X = 8X
-5 + 8X = (X + -5)(X + -7)

Reorder the terms:
-5 + 8X = (-5 + X)(X + -7)

Reorder the terms:
-5 + 8X = (-5 + X)(-7 + X)

Multiply (-5 + X) * (-7 + X)
-5 + 8X = (-5(-7 + X) + X(-7 + X))
-5 + 8X = ((-7 * -5 + X * -5) + X(-7 + X))
-5 + 8X = ((35 + -5X) + X(-7 + X))
-5 + 8X = (35 + -5X + (-7 * X + X * X))
-5 + 8X = (35 + -5X + (-7X + X2))

Combine like terms: -5X + -7X = -12X
-5 + 8X = (35 + -12X + X2)

Solving
-5 + 8X = 35 + -12X + X2

Solving for variable 'X'.

Reorder the terms:
-5 + -35 + 8X + 12X + -1X2 = 35 + -12X + X2 + -35 + 12X + -1X2

Combine like terms: -5 + -35 = -40
-40 + 8X + 12X + -1X2 = 35 + -12X + X2 + -35 + 12X + -1X2

Combine like terms: 8X + 12X = 20X
-40 + 20X + -1X2 = 35 + -12X + X2 + -35 + 12X + -1X2

Reorder the terms:
-40 + 20X + -1X2 = 35 + -35 + -12X + 12X + X2 + -1X2

Combine like terms: 35 + -35 = 0
-40 + 20X + -1X2 = 0 + -12X + 12X + X2 + -1X2
-40 + 20X + -1X2 = -12X + 12X + X2 + -1X2

Combine like terms: -12X + 12X = 0
-40 + 20X + -1X2 = 0 + X2 + -1X2
-40 + 20X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-40 + 20X + -1X2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
40 + -20X + X2 = 0

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -20X + -40 + X2 = 0 + -40

Reorder the terms:
40 + -40 + -20X + X2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -20X + X2 = 0 + -40
-20X + X2 = 0 + -40

Combine like terms: 0 + -40 = -40
-20X + X2 = -40

The X term is -20X.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20X + 100 + X2 = -40 + 100

Reorder the terms:
100 + -20X + X2 = -40 + 100

Combine like terms: -40 + 100 = 60
100 + -20X + X2 = 60

Factor a perfect square on the left side:
(X + -10)(X + -10) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(X + -10) equal to 7.745966692 and -7.745966692.

Subproblem 1
X + -10 = 7.745966692

Simplifying
X + -10 = 7.745966692

Reorder the terms:
-10 + X = 7.745966692

Solving
-10 + X = 7.745966692

Solving for variable 'X'.

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

Add '10' to each side of the equation.
-10 + 10 + X = 7.745966692 + 10

Combine like terms: -10 + 10 = 0
0 + X = 7.745966692 + 10
X = 7.745966692 + 10

Combine like terms: 7.745966692 + 10 = 17.745966692
X = 17.745966692

Simplifying
X = 17.745966692

Subproblem 2
X + -10 = -7.745966692

Simplifying
X + -10 = -7.745966692

Reorder the terms:
-10 + X = -7.745966692

Solving
-10 + X = -7.745966692

Solving for variable 'X'.

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

Add '10' to each side of the equation.
-10 + 10 + X = -7.745966692 + 10

Combine like terms: -10 + 10 = 0
0 + X = -7.745966692 + 10
X = -7.745966692 + 10

Combine like terms: -7.745966692 + 10 = 2.254033308
X = 2.254033308

Simplifying
X = 2.254033308

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {17.745966692, 2.254033308}