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

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


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

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

Reorder the terms:
((-12xy + 15x2) + 2y * (5x + -4y)) = 0
((-12xy + 15x2) + 2y * (5x + -4y)) = 0
(-12xy + 15x2 + (5x * 2y + -4y * 2y)) = 0
(-12xy + 15x2 + (10xy + -8y2)) = 0

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

Combine like terms: -12xy + 10xy = -2xy
(-2xy + 15x2 + -8y2) = 0

Solving
-2xy + 15x2 + -8y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(5x + -4y)' equal to zero and attempt to solve:

Simplifying
5x + -4y = 0

Solving
5x + -4y = 0

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

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

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

Divide each side by '5'.
x = 0.8y

Simplifying
x = 0.8y

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

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

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

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

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y
Solution
x = {0.8y, -0.6666666667y}

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