9(X-2)*2(2X-1)=8

Solution for 9(X-2)*2(2X-1)=8 equation:

Simplifying
9(X + -2) * 2(2X + -1) = 8

Reorder the terms:
9(-2 + X) * 2(2X + -1) = 8

Reorder the terms:
9(-2 + X) * 2(-1 + 2X) = 8

Reorder the terms for easier multiplication:
9 * 2(-2 + X)(-1 + 2X) = 8

Multiply 9 * 2
18(-2 + X)(-1 + 2X) = 8

Multiply (-2 + X) * (-1 + 2X)
18(-2(-1 + 2X) + X(-1 + 2X)) = 8
18((-1 * -2 + 2X * -2) + X(-1 + 2X)) = 8
18((2 + -4X) + X(-1 + 2X)) = 8
18(2 + -4X + (-1 * X + 2X * X)) = 8
18(2 + -4X + (-1X + 2X2)) = 8

Combine like terms: -4X + -1X = -5X
18(2 + -5X + 2X2) = 8
(2 * 18 + -5X * 18 + 2X2 * 18) = 8
(36 + -90X + 36X2) = 8

Solving
36 + -90X + 36X2 = 8

Solving for variable 'X'.

Reorder the terms:
36 + -8 + -90X + 36X2 = 8 + -8

Combine like terms: 36 + -8 = 28
28 + -90X + 36X2 = 8 + -8

Combine like terms: 8 + -8 = 0
28 + -90X + 36X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -45X + 18X2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(14 + -45X + 18X2)' equal to zero and attempt to solve:

Simplifying
14 + -45X + 18X2 = 0

Solving
14 + -45X + 18X2 = 0

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

Divide each side by '18'.
0.7777777778 + -2.5X + X2 = 0

Move the constant term to the right:

Add '-0.7777777778' to each side of the equation.
0.7777777778 + -2.5X + -0.7777777778 + X2 = 0 + -0.7777777778

Reorder the terms:
0.7777777778 + -0.7777777778 + -2.5X + X2 = 0 + -0.7777777778

Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000
0.0000000000 + -2.5X + X2 = 0 + -0.7777777778
-2.5X + X2 = 0 + -0.7777777778

Combine like terms: 0 + -0.7777777778 = -0.7777777778
-2.5X + X2 = -0.7777777778

The X term is -2.5X.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5X + 1.5625 + X2 = -0.7777777778 + 1.5625

Reorder the terms:
1.5625 + -2.5X + X2 = -0.7777777778 + 1.5625

Combine like terms: -0.7777777778 + 1.5625 = 0.7847222222
1.5625 + -2.5X + X2 = 0.7847222222

Factor a perfect square on the left side:
(X + -1.25)(X + -1.25) = 0.7847222222

Calculate the square root of the right side: 0.885845484

Break this problem into two subproblems by setting 
(X + -1.25) equal to 0.885845484 and -0.885845484.

Subproblem 1
X + -1.25 = 0.885845484

Simplifying
X + -1.25 = 0.885845484

Reorder the terms:
-1.25 + X = 0.885845484

Solving
-1.25 + X = 0.885845484

Solving for variable 'X'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + X = 0.885845484 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + X = 0.885845484 + 1.25
X = 0.885845484 + 1.25

Combine like terms: 0.885845484 + 1.25 = 2.135845484
X = 2.135845484

Simplifying
X = 2.135845484

Subproblem 2
X + -1.25 = -0.885845484

Simplifying
X + -1.25 = -0.885845484

Reorder the terms:
-1.25 + X = -0.885845484

Solving
-1.25 + X = -0.885845484

Solving for variable 'X'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + X = -0.885845484 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + X = -0.885845484 + 1.25
X = -0.885845484 + 1.25

Combine like terms: -0.885845484 + 1.25 = 0.364154516
X = 0.364154516

Simplifying
X = 0.364154516

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.135845484, 0.364154516}
Solution
X = {2.135845484, 0.364154516}