4x(2y-5x)=2y(x-y)

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


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

Reorder the terms:
4x(-5x + 2y) = 2y(x + -1y)
(-5x * 4x + 2y * 4x) = 2y(x + -1y)

Reorder the terms:
(8xy + -20x2) = 2y(x + -1y)
(8xy + -20x2) = 2y(x + -1y)
8xy + -20x2 = (x * 2y + -1y * 2y)
8xy + -20x2 = (2xy + -2y2)

Solving
8xy + -20x2 = 2xy + -2y2

Solving for variable 'x'.

Reorder the terms:
8xy + -2xy + -20x2 + 2y2 = 2xy + -2y2 + -2xy + 2y2

Combine like terms: 8xy + -2xy = 6xy
6xy + -20x2 + 2y2 = 2xy + -2y2 + -2xy + 2y2

Reorder the terms:
6xy + -20x2 + 2y2 = 2xy + -2xy + -2y2 + 2y2

Combine like terms: 2xy + -2xy = 0
6xy + -20x2 + 2y2 = 0 + -2y2 + 2y2
6xy + -20x2 + 2y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
6xy + -20x2 + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3xy + -10x2 + y2) = 0

Factor a trinomial.
2((-5x + -1y)(2x + -1y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5x + -1y)' equal to zero and attempt to solve:

Simplifying
-5x + -1y = 0

Solving
-5x + -1y = 0

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

Add 'y' to each side of the equation.
-5x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-5x + 0 = 0 + y
-5x = 0 + y
Remove the zero:
-5x = y

Divide each side by '-5'.
x = -0.2y

Simplifying
x = -0.2y

Subproblem 2
Set the factor '(2x + -1y)' equal to zero and attempt to solve:

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add 'y' to each side of the equation.
2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y
Solution
x = {-0.2y, 0.5y}

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