105=(4x-5)(2x-5)

Solution for 105=(4x-5)(2x-5) equation:

Simplifying
105 = (4x + -5)(2x + -5)

Reorder the terms:
105 = (-5 + 4x)(2x + -5)

Reorder the terms:
105 = (-5 + 4x)(-5 + 2x)

Multiply (-5 + 4x) * (-5 + 2x)
105 = (-5(-5 + 2x) + 4x * (-5 + 2x))
105 = ((-5 * -5 + 2x * -5) + 4x * (-5 + 2x))
105 = ((25 + -10x) + 4x * (-5 + 2x))
105 = (25 + -10x + (-5 * 4x + 2x * 4x))
105 = (25 + -10x + (-20x + 8x2))

Combine like terms: -10x + -20x = -30x
105 = (25 + -30x + 8x2)

Solving
105 = 25 + -30x + 8x2

Solving for variable 'x'.

Combine like terms: 105 + -25 = 80
80 + 30x + -8x2 = 25 + -30x + 8x2 + -25 + 30x + -8x2

Reorder the terms:
80 + 30x + -8x2 = 25 + -25 + -30x + 30x + 8x2 + -8x2

Combine like terms: 25 + -25 = 0
80 + 30x + -8x2 = 0 + -30x + 30x + 8x2 + -8x2
80 + 30x + -8x2 = -30x + 30x + 8x2 + -8x2

Combine like terms: -30x + 30x = 0
80 + 30x + -8x2 = 0 + 8x2 + -8x2
80 + 30x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
80 + 30x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + 15x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(40 + 15x + -4x2)' equal to zero and attempt to solve:

Simplifying
40 + 15x + -4x2 = 0

Solving
40 + 15x + -4x2 = 0

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

Divide each side by '-4'.
-10 + -3.75x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -3.75x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -3.75x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3.75x + x2 = 0 + 10
-3.75x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-3.75x + x2 = 10

The x term is -3.75x.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75x + 3.515625 + x2 = 10 + 3.515625

Reorder the terms:
3.515625 + -3.75x + x2 = 10 + 3.515625

Combine like terms: 10 + 3.515625 = 13.515625
3.515625 + -3.75x + x2 = 13.515625

Factor a perfect square on the left side:
(x + -1.875)(x + -1.875) = 13.515625

Calculate the square root of the right side: 3.676360292

Break this problem into two subproblems by setting 
(x + -1.875) equal to 3.676360292 and -3.676360292.

Subproblem 1
x + -1.875 = 3.676360292

Simplifying
x + -1.875 = 3.676360292

Reorder the terms:
-1.875 + x = 3.676360292

Solving
-1.875 + x = 3.676360292

Solving for variable 'x'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x = 3.676360292 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x = 3.676360292 + 1.875
x = 3.676360292 + 1.875

Combine like terms: 3.676360292 + 1.875 = 5.551360292
x = 5.551360292

Simplifying
x = 5.551360292

Subproblem 2
x + -1.875 = -3.676360292

Simplifying
x + -1.875 = -3.676360292

Reorder the terms:
-1.875 + x = -3.676360292

Solving
-1.875 + x = -3.676360292

Solving for variable 'x'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x = -3.676360292 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x = -3.676360292 + 1.875
x = -3.676360292 + 1.875

Combine like terms: -3.676360292 + 1.875 = -1.801360292
x = -1.801360292

Simplifying
x = -1.801360292

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.551360292, -1.801360292}
Solution
x = {5.551360292, -1.801360292}