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

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


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

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

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

Reorder the terms:
(5xy + 3xy + 3x2 + 5y2) = 0

Combine like terms: 5xy + 3xy = 8xy
(8xy + 3x2 + 5y2) = 0

Solving
8xy + 3x2 + 5y2 = 0

Solving for variable 'x'.

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


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

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y

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 = {-1y, -1.666666667y}

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