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

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


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

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

Reorder the terms:
((-10xy + 8x2) + -3y * (4x + -5y)) = 0
((-10xy + 8x2) + -3y * (4x + -5y)) = 0
(-10xy + 8x2 + (4x * -3y + -5y * -3y)) = 0
(-10xy + 8x2 + (-12xy + 15y2)) = 0

Reorder the terms:
(-10xy + -12xy + 8x2 + 15y2) = 0

Combine like terms: -10xy + -12xy = -22xy
(-22xy + 8x2 + 15y2) = 0

Solving
-22xy + 8x2 + 15y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(2x + -3y)' equal to zero and attempt to solve:

Simplifying
2x + -3y = 0

Solving
2x + -3y = 0

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

Add '3y' to each side of the equation.
2x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
2x + 0 = 0 + 3y
2x = 0 + 3y
Remove the zero:
2x = 3y

Divide each side by '2'.
x = 1.5y

Simplifying
x = 1.5y

Subproblem 2
Set the factor '(4x + -5y)' equal to zero and attempt to solve:

Simplifying
4x + -5y = 0

Solving
4x + -5y = 0

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

Add '5y' to each side of the equation.
4x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
4x + 0 = 0 + 5y
4x = 0 + 5y
Remove the zero:
4x = 5y

Divide each side by '4'.
x = 1.25y

Simplifying
x = 1.25y
Solution
x = {1.5y, 1.25y}

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