(x-5)(45-x-5)=4(x-55)

Solution for (x-5)(45-x-5)=4(x-55) equation:

Simplifying
(x + -5)(45 + -1x + -5) = 4(x + -55)

Reorder the terms:
(-5 + x)(45 + -1x + -5) = 4(x + -55)

Reorder the terms:
(-5 + x)(45 + -5 + -1x) = 4(x + -55)

Combine like terms: 45 + -5 = 40
(-5 + x)(40 + -1x) = 4(x + -55)

Multiply (-5 + x) * (40 + -1x)
(-5(40 + -1x) + x(40 + -1x)) = 4(x + -55)
((40 * -5 + -1x * -5) + x(40 + -1x)) = 4(x + -55)
((-200 + 5x) + x(40 + -1x)) = 4(x + -55)
(-200 + 5x + (40 * x + -1x * x)) = 4(x + -55)
(-200 + 5x + (40x + -1x2)) = 4(x + -55)

Combine like terms: 5x + 40x = 45x
(-200 + 45x + -1x2) = 4(x + -55)

Reorder the terms:
-200 + 45x + -1x2 = 4(-55 + x)
-200 + 45x + -1x2 = (-55 * 4 + x * 4)
-200 + 45x + -1x2 = (-220 + 4x)

Solving
-200 + 45x + -1x2 = -220 + 4x

Solving for variable 'x'.

Reorder the terms:
-200 + 220 + 45x + -4x + -1x2 = -220 + 4x + 220 + -4x

Combine like terms: -200 + 220 = 20
20 + 45x + -4x + -1x2 = -220 + 4x + 220 + -4x

Combine like terms: 45x + -4x = 41x
20 + 41x + -1x2 = -220 + 4x + 220 + -4x

Reorder the terms:
20 + 41x + -1x2 = -220 + 220 + 4x + -4x

Combine like terms: -220 + 220 = 0
20 + 41x + -1x2 = 0 + 4x + -4x
20 + 41x + -1x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
20 + 41x + -1x2 = 0

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

Divide each side by '-1'.
-20 + -41x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -41x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -41x + x2 = 0 + 20

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

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

The x term is -41x.  Take half its coefficient (-20.5).
Square it (420.25) and add it to both sides.

Add '420.25' to each side of the equation.
-41x + 420.25 + x2 = 20 + 420.25

Reorder the terms:
420.25 + -41x + x2 = 20 + 420.25

Combine like terms: 20 + 420.25 = 440.25
420.25 + -41x + x2 = 440.25

Factor a perfect square on the left side:
(x + -20.5)(x + -20.5) = 440.25

Calculate the square root of the right side: 20.982135258

Break this problem into two subproblems by setting 
(x + -20.5) equal to 20.982135258 and -20.982135258.

Subproblem 1
x + -20.5 = 20.982135258

Simplifying
x + -20.5 = 20.982135258

Reorder the terms:
-20.5 + x = 20.982135258

Solving
-20.5 + x = 20.982135258

Solving for variable 'x'.

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

Add '20.5' to each side of the equation.
-20.5 + 20.5 + x = 20.982135258 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + x = 20.982135258 + 20.5
x = 20.982135258 + 20.5

Combine like terms: 20.982135258 + 20.5 = 41.482135258
x = 41.482135258

Simplifying
x = 41.482135258

Subproblem 2
x + -20.5 = -20.982135258

Simplifying
x + -20.5 = -20.982135258

Reorder the terms:
-20.5 + x = -20.982135258

Solving
-20.5 + x = -20.982135258

Solving for variable 'x'.

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

Add '20.5' to each side of the equation.
-20.5 + 20.5 + x = -20.982135258 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + x = -20.982135258 + 20.5
x = -20.982135258 + 20.5

Combine like terms: -20.982135258 + 20.5 = -0.482135258
x = -0.482135258

Simplifying
x = -0.482135258

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {41.482135258, -0.482135258}