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

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


Simplifying
(3x + -1y)(x + y) = 0

Multiply (3x + -1y) * (x + y)
(3x * (x + y) + -1y * (x + y)) = 0
((x * 3x + y * 3x) + -1y * (x + y)) = 0

Reorder the terms:
((3xy + 3x2) + -1y * (x + y)) = 0
((3xy + 3x2) + -1y * (x + y)) = 0
(3xy + 3x2 + (x * -1y + y * -1y)) = 0
(3xy + 3x2 + (-1xy + -1y2)) = 0

Reorder the terms:
(3xy + -1xy + 3x2 + -1y2) = 0

Combine like terms: 3xy + -1xy = 2xy
(2xy + 3x2 + -1y2) = 0

Solving
2xy + 3x2 + -1y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -1y)(x + y) = 0


Subproblem 1
Set the factor '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y

Subproblem 2
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
Solution
x = {0.3333333333y, -1y}

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