0=(-2)*(40x-2x^2)+(50-2x)*(40-4x)

Solution for 0=(-2)*(40x-2x^2)+(50-2x)*(40-4x) equation:

Simplifying
0 = (-2)(40x + -2x2) + (50 + -2x)(40 + -4x)
0 = (40x * -2 + -2x2 * -2) + (50 + -2x)(40 + -4x)
0 = (-80x + 4x2) + (50 + -2x)(40 + -4x)

Multiply (50 + -2x) * (40 + -4x)
0 = -80x + 4x2 + (50(40 + -4x) + -2x * (40 + -4x))
0 = -80x + 4x2 + ((40 * 50 + -4x * 50) + -2x * (40 + -4x))
0 = -80x + 4x2 + ((2000 + -200x) + -2x * (40 + -4x))
0 = -80x + 4x2 + (2000 + -200x + (40 * -2x + -4x * -2x))
0 = -80x + 4x2 + (2000 + -200x + (-80x + 8x2))

Combine like terms: -200x + -80x = -280x
0 = -80x + 4x2 + (2000 + -280x + 8x2)

Reorder the terms:
0 = 2000 + -80x + -280x + 4x2 + 8x2

Combine like terms: -80x + -280x = -360x
0 = 2000 + -360x + 4x2 + 8x2

Combine like terms: 4x2 + 8x2 = 12x2
0 = 2000 + -360x + 12x2

Solving
0 = 2000 + -360x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + -2000 = -2000
-2000 + 360x + -12x2 = 2000 + -360x + 12x2 + -2000 + 360x + -12x2

Reorder the terms:
-2000 + 360x + -12x2 = 2000 + -2000 + -360x + 360x + 12x2 + -12x2

Combine like terms: 2000 + -2000 = 0
-2000 + 360x + -12x2 = 0 + -360x + 360x + 12x2 + -12x2
-2000 + 360x + -12x2 = -360x + 360x + 12x2 + -12x2

Combine like terms: -360x + 360x = 0
-2000 + 360x + -12x2 = 0 + 12x2 + -12x2
-2000 + 360x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-2000 + 360x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-500 + 90x + -3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-500 + 90x + -3x2)' equal to zero and attempt to solve:

Simplifying
-500 + 90x + -3x2 = 0

Solving
-500 + 90x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
166.6666667 + -30x + x2 = 0

Move the constant term to the right:

Add '-166.6666667' to each side of the equation.
166.6666667 + -30x + -166.6666667 + x2 = 0 + -166.6666667

Reorder the terms:
166.6666667 + -166.6666667 + -30x + x2 = 0 + -166.6666667

Combine like terms: 166.6666667 + -166.6666667 = 0.0000000
0.0000000 + -30x + x2 = 0 + -166.6666667
-30x + x2 = 0 + -166.6666667

Combine like terms: 0 + -166.6666667 = -166.6666667
-30x + x2 = -166.6666667

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -166.6666667 + 225

Reorder the terms:
225 + -30x + x2 = -166.6666667 + 225

Combine like terms: -166.6666667 + 225 = 58.3333333
225 + -30x + x2 = 58.3333333

Factor a perfect square on the left side:
(x + -15)(x + -15) = 58.3333333

Calculate the square root of the right side: 7.637626156

Break this problem into two subproblems by setting 
(x + -15) equal to 7.637626156 and -7.637626156.

Subproblem 1
x + -15 = 7.637626156

Simplifying
x + -15 = 7.637626156

Reorder the terms:
-15 + x = 7.637626156

Solving
-15 + x = 7.637626156

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 7.637626156 + 15

Combine like terms: -15 + 15 = 0
0 + x = 7.637626156 + 15
x = 7.637626156 + 15

Combine like terms: 7.637626156 + 15 = 22.637626156
x = 22.637626156

Simplifying
x = 22.637626156

Subproblem 2
x + -15 = -7.637626156

Simplifying
x + -15 = -7.637626156

Reorder the terms:
-15 + x = -7.637626156

Solving
-15 + x = -7.637626156

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -7.637626156 + 15

Combine like terms: -15 + 15 = 0
0 + x = -7.637626156 + 15
x = -7.637626156 + 15

Combine like terms: -7.637626156 + 15 = 7.362373844
x = 7.362373844

Simplifying
x = 7.362373844

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.637626156, 7.362373844}
Solution
x = {22.637626156, 7.362373844}