4(6-x-2)(3-x-5)=9(5-2x)

Solution for 4(6-x-2)(3-x-5)=9(5-2x) equation:

Simplifying
4(6 + -1x + -2)(3 + -1x + -5) = 9(5 + -2x)

Reorder the terms:
4(6 + -2 + -1x)(3 + -1x + -5) = 9(5 + -2x)

Combine like terms: 6 + -2 = 4
4(4 + -1x)(3 + -1x + -5) = 9(5 + -2x)

Reorder the terms:
4(4 + -1x)(3 + -5 + -1x) = 9(5 + -2x)

Combine like terms: 3 + -5 = -2
4(4 + -1x)(-2 + -1x) = 9(5 + -2x)

Multiply (4 + -1x) * (-2 + -1x)
4(4(-2 + -1x) + -1x * (-2 + -1x)) = 9(5 + -2x)
4((-2 * 4 + -1x * 4) + -1x * (-2 + -1x)) = 9(5 + -2x)
4((-8 + -4x) + -1x * (-2 + -1x)) = 9(5 + -2x)
4(-8 + -4x + (-2 * -1x + -1x * -1x)) = 9(5 + -2x)
4(-8 + -4x + (2x + 1x2)) = 9(5 + -2x)

Combine like terms: -4x + 2x = -2x
4(-8 + -2x + 1x2) = 9(5 + -2x)
(-8 * 4 + -2x * 4 + 1x2 * 4) = 9(5 + -2x)
(-32 + -8x + 4x2) = 9(5 + -2x)
-32 + -8x + 4x2 = (5 * 9 + -2x * 9)
-32 + -8x + 4x2 = (45 + -18x)

Solving
-32 + -8x + 4x2 = 45 + -18x

Solving for variable 'x'.

Reorder the terms:
-32 + -45 + -8x + 18x + 4x2 = 45 + -18x + -45 + 18x

Combine like terms: -32 + -45 = -77
-77 + -8x + 18x + 4x2 = 45 + -18x + -45 + 18x

Combine like terms: -8x + 18x = 10x
-77 + 10x + 4x2 = 45 + -18x + -45 + 18x

Reorder the terms:
-77 + 10x + 4x2 = 45 + -45 + -18x + 18x

Combine like terms: 45 + -45 = 0
-77 + 10x + 4x2 = 0 + -18x + 18x
-77 + 10x + 4x2 = -18x + 18x

Combine like terms: -18x + 18x = 0
-77 + 10x + 4x2 = 0

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

Divide each side by '4'.
-19.25 + 2.5x + x2 = 0

Move the constant term to the right:

Add '19.25' to each side of the equation.
-19.25 + 2.5x + 19.25 + x2 = 0 + 19.25

Reorder the terms:
-19.25 + 19.25 + 2.5x + x2 = 0 + 19.25

Combine like terms: -19.25 + 19.25 = 0.00
0.00 + 2.5x + x2 = 0 + 19.25
2.5x + x2 = 0 + 19.25

Combine like terms: 0 + 19.25 = 19.25
2.5x + x2 = 19.25

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 = 19.25 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 19.25 + 1.5625

Combine like terms: 19.25 + 1.5625 = 20.8125
1.5625 + 2.5x + x2 = 20.8125

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 20.8125

Calculate the square root of the right side: 4.562071898

Break this problem into two subproblems by setting 
(x + 1.25) equal to 4.562071898 and -4.562071898.

Subproblem 1
x + 1.25 = 4.562071898

Simplifying
x + 1.25 = 4.562071898

Reorder the terms:
1.25 + x = 4.562071898

Solving
1.25 + x = 4.562071898

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 = 4.562071898 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 4.562071898 + -1.25
x = 4.562071898 + -1.25

Combine like terms: 4.562071898 + -1.25 = 3.312071898
x = 3.312071898

Simplifying
x = 3.312071898

Subproblem 2
x + 1.25 = -4.562071898

Simplifying
x + 1.25 = -4.562071898

Reorder the terms:
1.25 + x = -4.562071898

Solving
1.25 + x = -4.562071898

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 = -4.562071898 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -4.562071898 + -1.25
x = -4.562071898 + -1.25

Combine like terms: -4.562071898 + -1.25 = -5.812071898
x = -5.812071898

Simplifying
x = -5.812071898

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.312071898, -5.812071898}