2x(2x-5y)-4x(5y-x)-9xy=0

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Solution for 2x(2x-5y)-4x(5y-x)-9xy=0 equation: 


Simplifying
2x(2x + -5y) + -4x(5y + -1x) + -9xy = 0
(2x * 2x + -5y * 2x) + -4x(5y + -1x) + -9xy = 0

Reorder the terms:
(-10xy + 4x2) + -4x(5y + -1x) + -9xy = 0
(-10xy + 4x2) + -4x(5y + -1x) + -9xy = 0

Reorder the terms:
-10xy + 4x2 + -4x(-1x + 5y) + -9xy = 0
-10xy + 4x2 + (-1x * -4x + 5y * -4x) + -9xy = 0

Reorder the terms:
-10xy + 4x2 + (-20xy + 4x2) + -9xy = 0
-10xy + 4x2 + (-20xy + 4x2) + -9xy = 0

Reorder the terms:
-10xy + -20xy + -9xy + 4x2 + 4x2 = 0

Combine like terms: -10xy + -20xy = -30xy
-30xy + -9xy + 4x2 + 4x2 = 0

Combine like terms: -30xy + -9xy = -39xy
-39xy + 4x2 + 4x2 = 0

Combine like terms: 4x2 + 4x2 = 8x2
-39xy + 8x2 = 0

Solving
-39xy + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-39y + 8x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-39y + 8x)' equal to zero and attempt to solve:

Simplifying
-39y + 8x = 0

Reorder the terms:
8x + -39y = 0

Solving
8x + -39y = 0

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

Add '39y' to each side of the equation.
8x + -39y + 39y = 0 + 39y

Combine like terms: -39y + 39y = 0
8x + 0 = 0 + 39y
8x = 0 + 39y
Remove the zero:
8x = 39y

Divide each side by '8'.
x = 4.875y

Simplifying
x = 4.875y
Solution
x = {0, 4.875y}

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