(5x-3y)(2x-4y)=0

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Solution for (5x-3y)(2x-4y)=0 equation: 


Simplifying
(5x + -3y)(2x + -4y) = 0

Multiply (5x + -3y) * (2x + -4y)
(5x * (2x + -4y) + -3y * (2x + -4y)) = 0
((2x * 5x + -4y * 5x) + -3y * (2x + -4y)) = 0

Reorder the terms:
((-20xy + 10x2) + -3y * (2x + -4y)) = 0
((-20xy + 10x2) + -3y * (2x + -4y)) = 0
(-20xy + 10x2 + (2x * -3y + -4y * -3y)) = 0
(-20xy + 10x2 + (-6xy + 12y2)) = 0

Reorder the terms:
(-20xy + -6xy + 10x2 + 12y2) = 0

Combine like terms: -20xy + -6xy = -26xy
(-26xy + 10x2 + 12y2) = 0

Solving
-26xy + 10x2 + 12y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-13xy + 5x2 + 6y2) = 0

Factor a trinomial.
2((x + -2y)(5x + -3y)) = 0

Ignore the factor 2.

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

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

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

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

Simplifying
x = 2y

Subproblem 2
Set the factor '(5x + -3y)' equal to zero and attempt to solve:

Simplifying
5x + -3y = 0

Solving
5x + -3y = 0

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

Add '3y' to each side of the equation.
5x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
5x + 0 = 0 + 3y
5x = 0 + 3y
Remove the zero:
5x = 3y

Divide each side by '5'.
x = 0.6y

Simplifying
x = 0.6y
Solution
x = {2y, 0.6y}

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