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

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


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

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

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

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

Combine like terms: 15xy + 15xy = 30xy
(30xy + 9x2 + 25y2) = 0

Solving
30xy + 9x2 + 25y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {-1.666666667y, -1.666666667y}

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