(5x+3y)(3x+5y)=0

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


Simplifying
(5x + 3y)(3x + 5y) = 0

Multiply (5x + 3y) * (3x + 5y)
(5x * (3x + 5y) + 3y * (3x + 5y)) = 0
((3x * 5x + 5y * 5x) + 3y * (3x + 5y)) = 0

Reorder the terms:
((25xy + 15x2) + 3y * (3x + 5y)) = 0
((25xy + 15x2) + 3y * (3x + 5y)) = 0
(25xy + 15x2 + (3x * 3y + 5y * 3y)) = 0
(25xy + 15x2 + (9xy + 15y2)) = 0

Reorder the terms:
(25xy + 9xy + 15x2 + 15y2) = 0

Combine like terms: 25xy + 9xy = 34xy
(34xy + 15x2 + 15y2) = 0

Solving
34xy + 15x2 + 15y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
3x + 5y = 0

Solving
3x + 5y = 0

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

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

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

Divide each side by '3'.
x = -1.666666667y

Simplifying
x = -1.666666667y
Solution
x = {-0.6y, -1.666666667y}

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