(100-y)*2y=200

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Solution for (100-y)*2y=200 equation: 


Simplifying
(100 + -1y) * 2y = 200

Reorder the terms for easier multiplication:
2y(100 + -1y) = 200
(100 * 2y + -1y * 2y) = 200
(200y + -2y2) = 200

Solving
200y + -2y2 = 200

Solving for variable 'y'.

Reorder the terms:
-200 + 200y + -2y2 = 200 + -200

Combine like terms: 200 + -200 = 0
-200 + 200y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-100 + 100y + -1y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-100 + 100y + -1y2)' equal to zero and attempt to solve:

Simplifying
-100 + 100y + -1y2 = 0

Solving
-100 + 100y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
100 + -100y + y2 = 0

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -100y + -100 + y2 = 0 + -100

Reorder the terms:
100 + -100 + -100y + y2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -100y + y2 = 0 + -100
-100y + y2 = 0 + -100

Combine like terms: 0 + -100 = -100
-100y + y2 = -100

The y term is -100y.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100y + 2500 + y2 = -100 + 2500

Reorder the terms:
2500 + -100y + y2 = -100 + 2500

Combine like terms: -100 + 2500 = 2400
2500 + -100y + y2 = 2400

Factor a perfect square on the left side:
(y + -50)(y + -50) = 2400

Calculate the square root of the right side: 48.989794856

Break this problem into two subproblems by setting 
(y + -50) equal to 48.989794856 and -48.989794856.


Subproblem 1
y + -50 = 48.989794856

Simplifying
y + -50 = 48.989794856

Reorder the terms:
-50 + y = 48.989794856

Solving
-50 + y = 48.989794856

Solving for variable 'y'.

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

Add '50' to each side of the equation.
-50 + 50 + y = 48.989794856 + 50

Combine like terms: -50 + 50 = 0
0 + y = 48.989794856 + 50
y = 48.989794856 + 50

Combine like terms: 48.989794856 + 50 = 98.989794856
y = 98.989794856

Simplifying
y = 98.989794856


Subproblem 2
y + -50 = -48.989794856

Simplifying
y + -50 = -48.989794856

Reorder the terms:
-50 + y = -48.989794856

Solving
-50 + y = -48.989794856

Solving for variable 'y'.

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

Add '50' to each side of the equation.
-50 + 50 + y = -48.989794856 + 50

Combine like terms: -50 + 50 = 0
0 + y = -48.989794856 + 50
y = -48.989794856 + 50

Combine like terms: -48.989794856 + 50 = 1.010205144
y = 1.010205144

Simplifying
y = 1.010205144


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {98.989794856, 1.010205144}
Solution
y = {98.989794856, 1.010205144}

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