(x-y)(3x-4y)=0

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Solution for (x-y)(3x-4y)=0 equation: 


Simplifying
(x + -1y)(3x + -4y) = 0

Multiply (x + -1y) * (3x + -4y)
(x(3x + -4y) + -1y * (3x + -4y)) = 0
((3x * x + -4y * x) + -1y * (3x + -4y)) = 0

Reorder the terms:
((-4xy + 3x2) + -1y * (3x + -4y)) = 0
((-4xy + 3x2) + -1y * (3x + -4y)) = 0
(-4xy + 3x2 + (3x * -1y + -4y * -1y)) = 0
(-4xy + 3x2 + (-3xy + 4y2)) = 0

Reorder the terms:
(-4xy + -3xy + 3x2 + 4y2) = 0

Combine like terms: -4xy + -3xy = -7xy
(-7xy + 3x2 + 4y2) = 0

Solving
-7xy + 3x2 + 4y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -4y)(x + -1y) = 0


Subproblem 1
Set the factor '(3x + -4y)' equal to zero and attempt to solve:

Simplifying
3x + -4y = 0

Solving
3x + -4y = 0

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

Add '4y' to each side of the equation.
3x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
3x + 0 = 0 + 4y
3x = 0 + 4y
Remove the zero:
3x = 4y

Divide each side by '3'.
x = 1.333333333y

Simplifying
x = 1.333333333y

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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y
Solution
x = {1.333333333y, y}

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