(4x-3y)(6x-y)=0

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Solution for (4x-3y)(6x-y)=0 equation: 


Simplifying
(4x + -3y)(6x + -1y) = 0

Multiply (4x + -3y) * (6x + -1y)
(4x * (6x + -1y) + -3y * (6x + -1y)) = 0
((6x * 4x + -1y * 4x) + -3y * (6x + -1y)) = 0

Reorder the terms:
((-4xy + 24x2) + -3y * (6x + -1y)) = 0
((-4xy + 24x2) + -3y * (6x + -1y)) = 0
(-4xy + 24x2 + (6x * -3y + -1y * -3y)) = 0
(-4xy + 24x2 + (-18xy + 3y2)) = 0

Reorder the terms:
(-4xy + -18xy + 24x2 + 3y2) = 0

Combine like terms: -4xy + -18xy = -22xy
(-22xy + 24x2 + 3y2) = 0

Solving
-22xy + 24x2 + 3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + -3y)(6x + -1y) = 0


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

Simplifying
4x + -3y = 0

Solving
4x + -3y = 0

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

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

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

Divide each side by '4'.
x = 0.75y

Simplifying
x = 0.75y

Subproblem 2
Set the factor '(6x + -1y)' equal to zero and attempt to solve:

Simplifying
6x + -1y = 0

Solving
6x + -1y = 0

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

Add 'y' to each side of the equation.
6x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
6x + 0 = 0 + y
6x = 0 + y
Remove the zero:
6x = y

Divide each side by '6'.
x = 0.1666666667y

Simplifying
x = 0.1666666667y
Solution
x = {0.75y, 0.1666666667y}

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