100-50x=(10-2x)2(4-x)

Solution for 100-50x=(10-2x)2(4-x) equation:

Simplifying
100 + -50x = (10 + -2x) * 2(4 + -1x)

Reorder the terms for easier multiplication:
100 + -50x = 2(10 + -2x)(4 + -1x)

Multiply (10 + -2x) * (4 + -1x)
100 + -50x = 2(10(4 + -1x) + -2x * (4 + -1x))
100 + -50x = 2((4 * 10 + -1x * 10) + -2x * (4 + -1x))
100 + -50x = 2((40 + -10x) + -2x * (4 + -1x))
100 + -50x = 2(40 + -10x + (4 * -2x + -1x * -2x))
100 + -50x = 2(40 + -10x + (-8x + 2x2))

Combine like terms: -10x + -8x = -18x
100 + -50x = 2(40 + -18x + 2x2)
100 + -50x = (40 * 2 + -18x * 2 + 2x2 * 2)
100 + -50x = (80 + -36x + 4x2)

Solving
100 + -50x = 80 + -36x + 4x2

Solving for variable 'x'.

Reorder the terms:
100 + -80 + -50x + 36x + -4x2 = 80 + -36x + 4x2 + -80 + 36x + -4x2

Combine like terms: 100 + -80 = 20
20 + -50x + 36x + -4x2 = 80 + -36x + 4x2 + -80 + 36x + -4x2

Combine like terms: -50x + 36x = -14x
20 + -14x + -4x2 = 80 + -36x + 4x2 + -80 + 36x + -4x2

Reorder the terms:
20 + -14x + -4x2 = 80 + -80 + -36x + 36x + 4x2 + -4x2

Combine like terms: 80 + -80 = 0
20 + -14x + -4x2 = 0 + -36x + 36x + 4x2 + -4x2
20 + -14x + -4x2 = -36x + 36x + 4x2 + -4x2

Combine like terms: -36x + 36x = 0
20 + -14x + -4x2 = 0 + 4x2 + -4x2
20 + -14x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
20 + -14x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -7x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(10 + -7x + -2x2)' equal to zero and attempt to solve:

Simplifying
10 + -7x + -2x2 = 0

Solving
10 + -7x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 3.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3.5x + x2 = 0 + 5
3.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
3.5x + x2 = 5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 5 + 3.0625

Combine like terms: 5 + 3.0625 = 8.0625
3.0625 + 3.5x + x2 = 8.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.839454173 and -2.839454173.

Subproblem 1
x + 1.75 = 2.839454173

Simplifying
x + 1.75 = 2.839454173

Reorder the terms:
1.75 + x = 2.839454173

Solving
1.75 + x = 2.839454173

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 2.839454173 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 2.839454173 + -1.75
x = 2.839454173 + -1.75

Combine like terms: 2.839454173 + -1.75 = 1.089454173
x = 1.089454173

Simplifying
x = 1.089454173

Subproblem 2
x + 1.75 = -2.839454173

Simplifying
x + 1.75 = -2.839454173

Reorder the terms:
1.75 + x = -2.839454173

Solving
1.75 + x = -2.839454173

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -2.839454173 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -2.839454173 + -1.75
x = -2.839454173 + -1.75

Combine like terms: -2.839454173 + -1.75 = -4.589454173
x = -4.589454173

Simplifying
x = -4.589454173

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.089454173, -4.589454173}
Solution
x = {1.089454173, -4.589454173}