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

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


Simplifying
(5x + -1y)(x + -3y) = 0

Multiply (5x + -1y) * (x + -3y)
(5x * (x + -3y) + -1y * (x + -3y)) = 0
((x * 5x + -3y * 5x) + -1y * (x + -3y)) = 0

Reorder the terms:
((-15xy + 5x2) + -1y * (x + -3y)) = 0
((-15xy + 5x2) + -1y * (x + -3y)) = 0
(-15xy + 5x2 + (x * -1y + -3y * -1y)) = 0
(-15xy + 5x2 + (-1xy + 3y2)) = 0

Reorder the terms:
(-15xy + -1xy + 5x2 + 3y2) = 0

Combine like terms: -15xy + -1xy = -16xy
(-16xy + 5x2 + 3y2) = 0

Solving
-16xy + 5x2 + 3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -3y)(5x + -1y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5x + -1y)' equal to zero and attempt to solve:

Simplifying
5x + -1y = 0

Solving
5x + -1y = 0

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

Add 'y' to each side of the equation.
5x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
5x + 0 = 0 + y
5x = 0 + y
Remove the zero:
5x = y

Divide each side by '5'.
x = 0.2y

Simplifying
x = 0.2y
Solution
x = {3y, 0.2y}

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