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

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


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

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

Reorder the terms:
((-1xy + 3x2) + 3y * (3x + -1y)) = 0
((-1xy + 3x2) + 3y * (3x + -1y)) = 0
(-1xy + 3x2 + (3x * 3y + -1y * 3y)) = 0
(-1xy + 3x2 + (9xy + -3y2)) = 0

Reorder the terms:
(-1xy + 9xy + 3x2 + -3y2) = 0

Combine like terms: -1xy + 9xy = 8xy
(8xy + 3x2 + -3y2) = 0

Solving
8xy + 3x2 + -3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -1y)(x + 3y) = 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 + 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 = {0.3333333333y, -3y}

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