75=2x(2x+(x-5))+2x+(x-5)

Solution for 75=2x(2x+(x-5))+2x+(x-5) equation:

Simplifying
75 = 2x(2x + (x + -5)) + 2x + (x + -5)

Reorder the terms:
75 = 2x(2x + (-5 + x)) + 2x + (x + -5)

Remove parenthesis around (-5 + x)
75 = 2x(2x + -5 + x) + 2x + (x + -5)

Reorder the terms:
75 = 2x(-5 + 2x + x) + 2x + (x + -5)

Combine like terms: 2x + x = 3x
75 = 2x(-5 + 3x) + 2x + (x + -5)
75 = (-5 * 2x + 3x * 2x) + 2x + (x + -5)
75 = (-10x + 6x2) + 2x + (x + -5)

Reorder the terms:
75 = -10x + 6x2 + 2x + (-5 + x)

Remove parenthesis around (-5 + x)
75 = -10x + 6x2 + 2x + -5 + x

Reorder the terms:
75 = -5 + -10x + 2x + x + 6x2

Combine like terms: -10x + 2x = -8x
75 = -5 + -8x + x + 6x2

Combine like terms: -8x + x = -7x
75 = -5 + -7x + 6x2

Solving
75 = -5 + -7x + 6x2

Solving for variable 'x'.

Combine like terms: 75 + 5 = 80
80 + 7x + -6x2 = -5 + -7x + 6x2 + 5 + 7x + -6x2

Reorder the terms:
80 + 7x + -6x2 = -5 + 5 + -7x + 7x + 6x2 + -6x2

Combine like terms: -5 + 5 = 0
80 + 7x + -6x2 = 0 + -7x + 7x + 6x2 + -6x2
80 + 7x + -6x2 = -7x + 7x + 6x2 + -6x2

Combine like terms: -7x + 7x = 0
80 + 7x + -6x2 = 0 + 6x2 + -6x2
80 + 7x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
80 + 7x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-13.33333333 + -1.166666667x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -1.166666667x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -1.166666667x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -1.166666667x + x2 = 0 + 13.33333333
-1.166666667x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-1.166666667x + x2 = 13.33333333

The x term is -1.166666667x.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667x + 0.3402777780 + x2 = 13.33333333 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = 13.33333333 + 0.3402777780

Combine like terms: 13.33333333 + 0.3402777780 = 13.673611108
0.3402777780 + -1.166666667x + x2 = 13.673611108

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 13.673611108

Calculate the square root of the right side: 3.697784622

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 3.697784622 and -3.697784622.

Subproblem 1
x + -0.5833333335 = 3.697784622

Simplifying
x + -0.5833333335 = 3.697784622

Reorder the terms:
-0.5833333335 + x = 3.697784622

Solving
-0.5833333335 + x = 3.697784622

Solving for variable 'x'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + x = 3.697784622 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = 3.697784622 + 0.5833333335
x = 3.697784622 + 0.5833333335

Combine like terms: 3.697784622 + 0.5833333335 = 4.2811179555
x = 4.2811179555

Simplifying
x = 4.2811179555

Subproblem 2
x + -0.5833333335 = -3.697784622

Simplifying
x + -0.5833333335 = -3.697784622

Reorder the terms:
-0.5833333335 + x = -3.697784622

Solving
-0.5833333335 + x = -3.697784622

Solving for variable 'x'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + x = -3.697784622 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = -3.697784622 + 0.5833333335
x = -3.697784622 + 0.5833333335

Combine like terms: -3.697784622 + 0.5833333335 = -3.1144512885
x = -3.1144512885

Simplifying
x = -3.1144512885

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.2811179555, -3.1144512885}