(3x+5y)(2x+6y)=

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Solution for (3x+5y)(2x+6y)= equation: 


Simplifying
(3x + 5y)(2x + 6y) = 0

Multiply (3x + 5y) * (2x + 6y)
(3x * (2x + 6y) + 5y * (2x + 6y)) = 0
((2x * 3x + 6y * 3x) + 5y * (2x + 6y)) = 0

Reorder the terms:
((18xy + 6x2) + 5y * (2x + 6y)) = 0
((18xy + 6x2) + 5y * (2x + 6y)) = 0
(18xy + 6x2 + (2x * 5y + 6y * 5y)) = 0
(18xy + 6x2 + (10xy + 30y2)) = 0

Reorder the terms:
(18xy + 10xy + 6x2 + 30y2) = 0

Combine like terms: 18xy + 10xy = 28xy
(28xy + 6x2 + 30y2) = 0

Solving
28xy + 6x2 + 30y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14xy + 3x2 + 15y2) = 0

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

Ignore the factor 2.

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 '(x + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

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

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

Simplifying
x = -3y
Solution
x = {-1.666666667y, -3y}

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