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

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


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

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

Reorder the terms:
((-6xy + 15x2) + -4y * (5x + -2y)) = 0
((-6xy + 15x2) + -4y * (5x + -2y)) = 0
(-6xy + 15x2 + (5x * -4y + -2y * -4y)) = 0
(-6xy + 15x2 + (-20xy + 8y2)) = 0

Reorder the terms:
(-6xy + -20xy + 15x2 + 8y2) = 0

Combine like terms: -6xy + -20xy = -26xy
(-26xy + 15x2 + 8y2) = 0

Solving
-26xy + 15x2 + 8y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -4y)(5x + -2y) = 0


Subproblem 1
Set the factor '(3x + -4y)' equal to zero and attempt to solve:

Simplifying
3x + -4y = 0

Solving
3x + -4y = 0

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

Add '4y' to each side of the equation.
3x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
3x + 0 = 0 + 4y
3x = 0 + 4y
Remove the zero:
3x = 4y

Divide each side by '3'.
x = 1.333333333y

Simplifying
x = 1.333333333y

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

Simplifying
5x + -2y = 0

Solving
5x + -2y = 0

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

Add '2y' to each side of the equation.
5x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
5x + 0 = 0 + 2y
5x = 0 + 2y
Remove the zero:
5x = 2y

Divide each side by '5'.
x = 0.4y

Simplifying
x = 0.4y
Solution
x = {1.333333333y, 0.4y}

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