(3x-y)(8x-y)=0

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Solution for (3x-y)(8x-y)=0 equation: 


Simplifying
(3x + -1y)(8x + -1y) = 0

Multiply (3x + -1y) * (8x + -1y)
(3x * (8x + -1y) + -1y * (8x + -1y)) = 0
((8x * 3x + -1y * 3x) + -1y * (8x + -1y)) = 0

Reorder the terms:
((-3xy + 24x2) + -1y * (8x + -1y)) = 0
((-3xy + 24x2) + -1y * (8x + -1y)) = 0
(-3xy + 24x2 + (8x * -1y + -1y * -1y)) = 0
(-3xy + 24x2 + (-8xy + 1y2)) = 0

Reorder the terms:
(-3xy + -8xy + 24x2 + 1y2) = 0

Combine like terms: -3xy + -8xy = -11xy
(-11xy + 24x2 + 1y2) = 0

Solving
-11xy + 24x2 + 1y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -1y)(8x + -1y) = 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 '(8x + -1y)' equal to zero and attempt to solve:

Simplifying
8x + -1y = 0

Solving
8x + -1y = 0

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

Add 'y' to each side of the equation.
8x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
8x + 0 = 0 + y
8x = 0 + y
Remove the zero:
8x = y

Divide each side by '8'.
x = 0.125y

Simplifying
x = 0.125y
Solution
x = {0.3333333333y, 0.125y}

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