(2-5x)(1-x)-(4-x)(4+x)=

Solution for (2-5x)(1-x)-(4-x)(4+x)= equation:

Simplifying
(2 + -5x)(1 + -1x) + -1(4 + -1x)(4 + x) = 0

Multiply (2 + -5x) * (1 + -1x)
(2(1 + -1x) + -5x * (1 + -1x)) + -1(4 + -1x)(4 + x) = 0
((1 * 2 + -1x * 2) + -5x * (1 + -1x)) + -1(4 + -1x)(4 + x) = 0
((2 + -2x) + -5x * (1 + -1x)) + -1(4 + -1x)(4 + x) = 0
(2 + -2x + (1 * -5x + -1x * -5x)) + -1(4 + -1x)(4 + x) = 0
(2 + -2x + (-5x + 5x2)) + -1(4 + -1x)(4 + x) = 0

Combine like terms: -2x + -5x = -7x
(2 + -7x + 5x2) + -1(4 + -1x)(4 + x) = 0

Multiply (4 + -1x) * (4 + x)
2 + -7x + 5x2 + -1(4(4 + x) + -1x * (4 + x)) = 0
2 + -7x + 5x2 + -1((4 * 4 + x * 4) + -1x * (4 + x)) = 0
2 + -7x + 5x2 + -1((16 + 4x) + -1x * (4 + x)) = 0
2 + -7x + 5x2 + -1(16 + 4x + (4 * -1x + x * -1x)) = 0
2 + -7x + 5x2 + -1(16 + 4x + (-4x + -1x2)) = 0

Combine like terms: 4x + -4x = 0
2 + -7x + 5x2 + -1(16 + 0 + -1x2) = 0
2 + -7x + 5x2 + -1(16 + -1x2) = 0
2 + -7x + 5x2 + (16 * -1 + -1x2 * -1) = 0
2 + -7x + 5x2 + (-16 + 1x2) = 0

Reorder the terms:
2 + -16 + -7x + 5x2 + 1x2 = 0

Combine like terms: 2 + -16 = -14
-14 + -7x + 5x2 + 1x2 = 0

Combine like terms: 5x2 + 1x2 = 6x2
-14 + -7x + 6x2 = 0

Solving
-14 + -7x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-2.333333333 + -1.166666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -1.166666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -1.166666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -1.166666667x + x2 = 0 + 2.333333333
-1.166666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-1.166666667x + x2 = 2.333333333

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 = 2.333333333 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = 2.333333333 + 0.3402777780

Combine like terms: 2.333333333 + 0.3402777780 = 2.673611111
0.3402777780 + -1.166666667x + x2 = 2.673611111

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 2.673611111

Calculate the square root of the right side: 1.635118072

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 1.635118072 and -1.635118072.

Subproblem 1
x + -0.5833333335 = 1.635118072

Simplifying
x + -0.5833333335 = 1.635118072

Reorder the terms:
-0.5833333335 + x = 1.635118072

Solving
-0.5833333335 + x = 1.635118072

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 = 1.635118072 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = 1.635118072 + 0.5833333335
x = 1.635118072 + 0.5833333335

Combine like terms: 1.635118072 + 0.5833333335 = 2.2184514055
x = 2.2184514055

Simplifying
x = 2.2184514055

Subproblem 2
x + -0.5833333335 = -1.635118072

Simplifying
x + -0.5833333335 = -1.635118072

Reorder the terms:
-0.5833333335 + x = -1.635118072

Solving
-0.5833333335 + x = -1.635118072

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 = -1.635118072 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = -1.635118072 + 0.5833333335
x = -1.635118072 + 0.5833333335

Combine like terms: -1.635118072 + 0.5833333335 = -1.0517847385
x = -1.0517847385

Simplifying
x = -1.0517847385

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2184514055, -1.0517847385}